· the activity group on nonlinear waves & coherent structures (nwcs) fosters collaborations...

The Activity Group on Nonlinear Waves & Coherent Structures (NWCS) fosters collaborations among applied mathematicians, physicists, fluid dynamicists, engineers, and biologists in those areas of research related to the theory, development, and use of nonlinear waves and coherent structures. It promotes and facilitates nonlinear waves and coherent structures as an academic discipline; brokers partnerships between academia, industry, and government laboratories; and works with other professional societies to promote NWCS.

The activity group organizes the biennial SIAM Conference on Nonlinear Waves & Coherent Structures; awards The Martin Kruskal Lecture every two years to recognize a notable body of mathematics and contributions in the field of nonlinear waves and coherent structures; and maintains a website, a member directory, and an electronic mailing list.

Final Program and Abstracts

Society for Industrial and Applied Mathematics3600 Market Street, 6th Floor

Philadelphia, PA 19104-2688 USATelephone: +1-215-382-9800 Fax: +1-215-386-7999

Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/

Membership and Customer Service: (800) 447-7426 (US & Canada) or +1-215-382-9800 (worldwide)

www.siam.org/meetings/nw14

Sponsored by the SIAM Activity Group on Nonlinear Waves and Coherent Structures.

This conference is being held in cooperation with the Institute of Mathematics and its Applications (IMA).

2 2014 SIAM Conference on Nonlinear Waves and Coherent Structures

Table of Contents

Program-at-a-Glance ... Separate handout

General Information .............................. 2

Get-togethers ......................................... 4

Invited Plenary Presentations ................ 6

Prize Lecture ......................................... 8

Program Schedule ................................. 9

Poster Session ..................................... 32

Abstracts ............................................. 57

Speaker and Organizer Index ............ 139

Conference Budget ... Inside Back Cover

Campus Map ........................ Back Cover

Organizing Committee Co-ChairsPaul Milewski University of Bath, United Kingdom

Beatrice PelloniUniversity of Reading, United Kingdom

(IMA representative)

Organizing CommitteeMargaret BeckBoston University, USA and Heriot-Watt

University, United Kingdom

Alina ChertockNorth Carolina State University, USA

Gadi FibichTel-Aviv University, Israel

Philip MainiUniversity of Oxford, United Kingdom

Apala MajumdarUniversity of Bath, United Kingdom

Sheehan OlverUniversity of Sydney, Australia

Barbara PrinariUniversity of Colorado, USA and Universitá

del Salento, Italy

Laurette TuckermanESPCI, France

Jianke YangUniversity of Vermont, USA

SIAM Registration Desk The SIAM registration desk is located in the Main Foyer - Concourse (Ground Floor). It is open during the following hours:

Sunday, August 10

5:00 PM - 7:00 PM

Monday, August 11

7:00 AM - 5:00 PM

Tuesday, August 12

7:45 AM - 5:00 PM

Wednesday, August 13

7:45 AM - 5:00 PM

Thursday, August 14

7:45 AM - 5:00 PM

Conference LocationAll sessions and on-site registration will take place on the main campus of Churchill College. A campus map is located online at https://www.chu.cam.ac.uk/student-hub/resources/college-map/, and is also included on the back of this program.

The website for the Churchill College is https://www.chu.cam.ac.uk/.

Churchill College Housing Telephone NumberIn the event of an emergency, messages may be left for attendees staying in Churchill College housing at 00 44 (0)1223 336000.

Child CareThe childcare office at the University of Cambridge operates the Cambridge Universities Holiday Playscheme for school age children, and delegates are invited to book places on the summer Playscheme. For more information on Playscheme please go to: www.cam.ac.uk/playscheme.

Attendees planning to bring their child and book accommodation at Churchill College should have received permission from the Bursar. The Bursar needs to review and consider all requests to bring children to the college. An adult must be with the child at all times, and each child must share a bedroom with an adult. All requests must have been made by July 14, 2014. Child care arrangements may not be made onsite.

Corporate Members and AffiliatesSIAM corporate members provide their employees with knowledge about, access to, and contacts in the applied mathematics and computational sciences community through their membership benefits. Corporate membership is more than just a bundle of tangible products and services; it is an expression of support for SIAM and its programs. SIAM is pleased to acknowledge its corporate members and sponsors. In recognition of their support, non-member attendees who are employed by the following organizations are entitled to the SIAM member registration rate.

2014 SIAM Conference on Nonlinear Waves and Coherent Structures 3

Corporate Institutional MembersThe Aerospace Corporation

Air Force Office of Scientific Research

AT&T Laboratories - Research

Bechtel Marine Propulsion Laboratory

The Boeing Company

CEA/DAM

Department of National Defence (DND/CSEC)

DSTO- Defence Science and Technology Organisation

Hewlett-Packard

IBM Corporation

IDA Center for Communications Research, La Jolla

IDA Center for Communications Research, Princeton

Institute for Computational and Experimental Research in Mathematics (ICERM)

Institute for Defense Analyses, Center for Computing Sciences

Lawrence Berkeley National Laboratory

Lockheed Martin

Los Alamos National Laboratory

Mathematical Sciences Research Institute

Max-Planck-Institute for Dynamics of Complex Technical Systems

Mentor Graphics

National Institute of Standards and Technology (NIST)

National Security Agency (DIRNSA)

Oak Ridge National Laboratory, managed by UT-Battelle for the Department of Energy

Sandia National Laboratories

Schlumberger-Doll Research

Tech X Corporation

U.S. Army Corps of Engineers, Engineer Research and Development Center

United States Department of Energy

List current June 2014

Funding AgenciesSIAM and the Conference Organizing Committee wish to extend their thanks and appreciation to the U.S. National Science Foundation and the Office of Naval Research Global (ONRG) for their support of this conference.

Join SIAM and save!

Leading the applied mathematics community . . .Join your peers in supporting the premier professional society for applied mathematicians and computational scientists. SIAM members receive subscriptions to SIAM Review, SIAM News and Unwrapped, and enjoy substantial discounts on SIAM books, journal subscriptions, and conference registrations.

Free Student Memberships are available to students who attend an institution that is an Academic Member of SIAM, are members of Student Chapters of SIAM, or are nominated by a nonstudent member of SIAM.

Join online or download an application form at www.siam.org/joinsiam, or contact SIAM Customer Service:

Telephone: +1-215-382-9800 (worldwide); or 800-447-7426 (U.S. and Canada only)

Fax: +1-215-386-7999

E-mail: [email protected]

Postal mail: Society for Industrial and Applied Mathematics, 3600 Market Street, 6th floor, Philadelphia, PA 19104-2688 USA

Standard Audio/Visual Set-Up in Meeting Rooms Each meeting room is equipped with an LCD projector, screen, whiteboard and flip chart.

SIAM does not provide computers, however, Wolfson Auditorium is equipped with one PC which will be made available to presenters speaking in this room. All other speakers must provide their own computers. Additionally, speakers must provide their own cables/adaptors to connect to the LCD projectors. A VGA input cable is the standard cable required to connect to the data projectors.

SIAM, Churchill College and JRA are not responsible for the safety and security of speakers’ computers.

Plenary Sessions Live StreamingThe plenary sessions will be streamed live from Jock Colville Hall, located in the Archives Center. If there is limited seating in Wolfson Hall, attendees are encouraged to view the presentation from Jock Colville Hall.

Internet AccessComplimentary high-speed wireless Internet access is available at Churchill College. To access Churchill College wireless Internet, select the “Churchill College” network. You do not need a password to access the wifi.

Churchill College is planning to have wireless Internet access available in ensuite bedrooms by July 2014. At the time of the publication, Internet access is available in all bedrooms via an Ethernet cable point. Cables are available to purchase from the Porters’ Lodge or delegates can bring their own.


Conference Registration Fee Includes• Admission to all technical sessions

• Business Meeting (open to SIAG/NWCS members)

• Internet access

• Morning and afternoon tea, coffee and biscuits daily

• Reception and Poster Session

• Room set-ups and audio/visual equipment

Job PostingsPlease check with the SIAM registration desk regarding the availability of job postings or visit http://jobs.siam.org.

Important Notice to Poster PresentersThe poster session is scheduled for Tuesday, August 12, 8:00 PM - 10:00 PM. Presenters are requested to put up their posters no later than 8:00 PM on Tuesday, the official start time of the session. Boards will be available to presenters beginning at 9:00 AM on Monday, August 11. Posters must be removed by 5:00 PM on Thursday, August 14.

Poster boards will be 1m wide x 2m high. Attendees are responsible for providing their own Velcro to adhere to the poster board.

SIAM Books and JournalsDisplay copies of books and complimentary copies of journals will be available on site. SIAM books are available at a discounted price during the conference. Titles on Display forms will be available with instructions on how to place a book order.

Name BadgesA space for emergency contact information is provided on the back of your name badge. Help us help you in the event of an emergency!

Comments?Comments about SIAM meetings are encouraged! Please send to:

Cynthia Phillips, SIAM Vice President for Programs ([email protected]).

Get-togethers • Reception and Poster Session

Tuesday, August 12

8:00 PM - 10:00 PM

• SIAG/NWCS Business Meeting (open to SIAG/NWCS members)


8:00 PM - 8:45 PM

Complimentary beer and wine will be served.

Please NoteSIAM, Churchill College and JRA are not responsible for the safety and security of attendees’ computers. Do not leave your laptop computers unattended. Please remember to turn off your cell phones, pagers, etc. during sessions.

Recording of PresentationsAudio and video recording of presentations at SIAM meetings is prohibited without the written permission of the presenter and SIAM.

Social MediaSIAM is promoting the use of social media, such as Facebook and Twitter, in order to enhance scientific discussion at its meetings and enable attendees to connect with each other prior to, during and after conferences. If you are tweeting about a conference, please

use the designated hashtag to enable other attendees to keep up with the Twitter conversation and to allow better archiving of our conference discussions. The hashtag for this meeting is #SIAMNW14.


SIAM Activity Group on Nonlinear Waves and Coherent Structure (SIAG/NWCS) www.siam.org/activity/nwcs

A GREAT WAY TO GET INVOLVED! Collaborate and interact with mathematicians and applied scientists whose work involves nonlinear waves and coherent structures.

ACTIVITIES INCLUDE:• Special sessions at SIAM Annual Meetings• Biennial conference • Martin D. Kruskal Lecture• Website

BENEFITS OF SIAG/NWSC membership:• Listing in the SIAG’s online membership directory • Additional $10 discount on registration at the SIAM Conference

on Nonlinear Waves and Coherent Structures (excludes student) • Electronic communications about recent developments in your

specialty• Eligibility for candidacy for SIAG/NWCS office• Participation in the selection of SIAG/NWCS officers

ELIGIBILITY:• Be a current SIAM member.

COST:• $10 per year• Student members can join two activity groups for free!

TO JOIN:

SIAG/NWCS: my.siam.org/forms/join_siag.htm

SIAM: www.siam.org/joinsiam

2013-14 SIAG/NWCS OFFICERS• Chair: Edgar Knobloch, University of California Berkeley• Vice Chair: Margaret Beck, Boston University• Program Director: Paul Milewski, University of Bath• Secretary: Richard Moore, New Jersey Institute of Technology

JOIN


Invited Plenary Speakers** All Invited Plenary Presentations will take place in Wolfson Auditorium - Wolfson Hall**

Monday, August 1110:45 AM - 11:30 AM

IP1 Stability and Synchrony in the Kuramoto Model Jared Bronski, University of Illinois at Urbana-Champaign, USA

1:00 PM - 1:45 PM

IP2 Integrability: Initial- Boundary Value Problems in 1+1, and Solitons in 3+1 Thanasis Fokas, University of Cambridge, United Kingdom

Tuesday, August 1210:45 AM - 11:30 AM

IP3 Minimal Models for Precipitating Convection

Leslie Smith, University of Wisconsin, USA

1:00 PM - 1:45 PM

IP4 Coherent Structures in 2D Turbulence: Identification and their Use

Rich Kerswell, University of Bristol, United Kingdom


Invited Plenary Speakers** All Invited Plenary Presentations will take place in Wolfson Auditorium - Wolfson Hall**

Wednesday, August 1310:45 AM - 11:30 AM

IP5 A Neural Field Model of Binocular Rivalry Waves

Paul C. Bressloff, University of Utah, USA and University of Oxford, United Kingdom

1:00 PM - 1:45 PM

IP6 Engineering Extreme Materials with Defects and Nonlinearity

Chiara Daraio, ETH Zürich, Switzerland and California Institute of Technology, USA

Thursday, August 1410:45 AM - 11:30 AM

IP7 Momentum Maps, Shape Analysis and Solitons

Darryl D. Holm, Imperial College London, United Kingdom and Los Alamos National Laboratory, USA

1:00 PM - 1:45 PM

IP8 Symmetry, Modulation and Nonlinear Waves

Tom J. Bridges, University of Surrey, United Kingdom


Prize LectureI

** The Prize Lecture will take place in Wolfson Auditorium - Wolfson Hall**

Monday, August 11

8:15 PM - 9:00 PM

SP1: Martin D. Kruskal Prize Lecture - Nonlinear Waves from Beaches to Photonics

Based on work of Kruskal et al the Korteweg-deVries equation was found to have many remarkable properties. These properties are shared by many other equations including the 2D Kadomtsev-Petvishvili (KP) equation, which arises in the study of shallow water waves.

Some solutions of KP and their relation to waves on shallow beaches will be discussed. Nonlinear waves in photonic periodic lattices will also be described; “photonic graphene” is a remarkable case. Since this is an evening lecture, equations and details will be kept to

a minimum, and the lecture will be colloquium style.

Mark Ablowitz, University of Colorado, USA


NW14 Program


Sunday, August 10

Registration5:00 PM-7:00 PMRoom:Main Foyer - Concourse (Ground Floor)

Monday, August 11

Registration7:00 AM-5:00 PMRoom:Main Foyer - Concourse (Ground Floor)

Monday, August 11

MS1Boundary-value Problems for Linear and Nonlinear Integrable Problems - Part I of III8:00 AM-10:00 AMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS9 In the last decade the use of a new method for solving boundary value problems due to Fokas has been expanded by him, his collaborators, and others. This method contains the classical solution methods as special cases and allows for the explicit solution of problems which could not previously be solved. This session will bring together practitioners of the Fokas Method and expose interested parties to the many applications of this technique.

Organizer: Natalie E. SheilsUniversity of Washington, USA

Organizer: Bernard DeconinckUniversity of Washington, USA

8:00-8:25 The Fokas Method for Interface ProblemsNatalie E. Sheils, University of Washington,

USA

8:30-8:55 The Unified Transform for the NLS with t-Periodic Boundary ConditionsAthanassios S. Fokas, University of

Cambridge, United Kingdom

9:00-9:25 The Initial Value Problem in Analytic Spaces of Nonlinear Evolution Equations with Traveling Wave SolutionsAlex Himonas, University of Notre Dame,

USA

9:30-9:55 On Rigorous Aspects of the Unified Transform MethodDionyssis Mantzavinos, University of Notre

Dame, USA


Monday, August 11

MS2Novel Challenges in Atomic Gases: Bose-Einstein condensates and Beyond8:00 AM-10:00 AMRoom:Jock Colville Hall - Archives Center

In recent years, we have witnessed novel developments in the field of ultracold quantum gases. These have spanned a wide range of directions including spin-orbit Bose-Einstein condensates, Dirac-type systems, Bose-Fermi mixtures, and exciton-polariton condensates and their solitary wave excitations (solitons, vortices, vortex rings). This minisymposium touches, via a diverse cohort of experts, upon the current state-of-the-art in this field and the challenges that lie ahead. A balanced perspective encompassing theory, computation and experiment will be sought that should be of value to newcomers, as well as to seasoned researchers in the field.

Organizer: Ricardo CarreteroSan Diego State University, USA

Organizer: Panayotis KevrekidisUniversity of Massachusetts, Amherst, USA

8:00-8:25 Pattern Formation in Solid State CondensatesNatalia G. Berloff, University of


8:30-8:55 Motion in a Bose-Einstein Condensate: Vortices, Turbulence and WakesCarlo F. Barenghi, George Stagg, and Nick

G. Parker, Newcastle University, United Kingdom

9:00-9:25 Intrinsic Photoconductivity of Ultracold Fermions in An Optical LatticeChristoph Becker, Jannes Heinze, Jasper

Krauser, Nick Flaeschner, Soeren Goetze, Alexander Itin, Ludwig Mathey, and Klaus Sengstlock, Universitat Hamburg, Germany

9:30-9:55 Quantum Hall Effect and Transport Phenomena in Lossy Photonic LatticesTomoki Ozawa, Universita di Trento, Italy

Monday, August 11

MS3Large Time Behavior in Schrödinger Equations from Different Perspectives - Part I of III8:00 AM-10:00 AMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS11 Partial differential equations of linear and/or nonlinear Schrödinger type furnish a canonical description of wave propagation in dispersive media. These equations have numerous applications, ranging from quantum mechanics, fiber optics, plasma physics and the description of water waves. One of the most important problems in the mathematical analysis of these equations concerns the precise description of solutions over long times. The proposed minisymposium will bring together experts in the analysis of Schrödinger equations who will give an overview of the current state-of-the art of the mathematical theory invoking several different perspectives, such as stochastics, geometry, and high frequency analysis.

Organizer: Christof SparberUniversity of Illinois, Chicago, USA

Organizer: Remi CarlesCNRS & Universite Montpellier 2, France

8:00-8:25 Scattering for Nonlinear Schrödinger Equations under Partial Harmonic ConfinementRemi Carles, CNRS & Universite

Montpellier 2, France

8:30-8:55 On the Long-Time Behavior of NLS in the Partially Periodic SettingNicola Visciglia, University of Pisa, Italy

9:00-9:25 Asymptotic Stability for Nls with Nonlinear Point InteractionsRiccardo Adami, Politecnico di Torino,

Italy

9:30-9:55 Some Collision Problems Related to Nonlinear Schrödinger EquationsClaudio Munoz, University of Paris, Orsay,

France

Monday, August 11

MS4Nonlinear Dynamics of Granular Crystals - Part I of II8:00 AM-10:00 AMRoom:Recital Room - Music Center

For Part 2 see MS12 Granular crystals are defined as ordered aggregates of elastically interacting particles. They can be assembled as homogeneous, heterogeneous, one-dimensional or even higher dimensional structures and can be tailored to have tunable nonlinear responses. This tunability makes granular crystals relevant for a host of engineering applications, including e.g. shock absorbing layers, acoustic lenses and sound scramblers. In that light, and in connection also to the plenary talk by Professor Chiara Daraio, the aim of this minisymposium is to bring together researchers studying problems in this field with view points from application, experiment, computation and analysis.

Organizer: Christopher ChongUniversity of Massachusetts, Amherst, USA

Organizer: Miguel MoleronETH Zürich, Switzerland

8:00-8:25 Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear LatticesChristopher Chong, University of

Massachusetts, Amherst, USA; Panayotis Kevrekidis, University of Massachusetts, Amherst, USA; Guido Schneider, University of Stuttgart, Germany

8:30-8:55 Acoustic Wave Filtering and Breather Formation in Coupled Granular Chains Embedded in Material MatrixAlexander Vakakis, M. Arif Hasan,

Sinhu Cho, D. Michael McFarland, and Waltraud M. Kriven, University of Illinois, USA

continued on next page


Monday, August 11

MS6Waves in Cell and Developmental Biology8:00 AM-10:00 AMRoom:Bevin Room - Wolfson Hall

Ever since the seminal work of Hodgkin-Huxley on the axonal propagation of action potentials, cell biology has been a major source of interesting problems in the mathematical modeling and analysis of nonlinear waves. In recent years there has been a growing interest in the functional role of intracellular and intercellular waves, based on variations in the concentration of signaling molecules (calcium, kinases, phosphotases, morphogens) and cytoskeletal structures. Applications include cell polarization, cell motility, cell growth, synaptic plasticity, neuronal development, and embryogenesis. We review some of these applications in this minisymposium.

Organizer: Paul C. BressloffUniversity of Utah, USA and University of Oxford, United Kingdom

8:00-8:25 Clock and Wavefront Model of SomitogenesisRuth E. Baker, University of Oxford,

United Kingdom

8:30-8:55 Actin Polymerization and Subcellular Mechanics Drive Nonlocal Excitable Waves in Living CellsJun Allard, University of California, Irvine,

USA

9:00-9:25 Actin Nucleation Waves in Motile CellsWilliam R. Holmes, University of

California, Irvine, USA

9:30-9:55 Ca2+/calmodulin-Dependent Protein Kinase Waves in Heterogeneous Spiny DendritesPaul C. Bressloff, University of Utah,

USA and University of Oxford, United Kingdom

Monday, August 11

MS4Nonlinear Dynamics of Granular Crystals - Part I of II8:00 AM-10:00 AMcontinued

9:00-9:25 An Asymptotic Model for Small Amplitude Solutions to Newton’s CradleBrigitte Bidegaray-Fesquet, CNRS

and Grenoble University, France; Eric Dumas and Guillaume James, Université de Grenoble and CNRS, France

9:30-9:55 Transitions from Energy Entrapment to Energy Transport in the System of N Coupled Granular ChainsYuli Starosvetsky, Technion - Israel

Institute of Technology, Israel

Monday, August 11

MS5SPDEs and Patterns8:00 AM-10:00 AMRoom:Club Room - Concourse (1st Floor)

Patterns and waves arise in many physical applications. A wide range of theoretical and numerical approaches have been developed for understanding their formation and dynamics in deterministic spatially extended PDEs. Less is known about the influence of noise on patterns and nonlinear waves. This minisymposium aims to bring together the ‘deterministic’ and ‘stochastic’ communities interested in SPDEs, pattern formation and wave dynamics with the goal of identifying common directions and problems.

Organizer: Christian KuehnVienna University of Technology, Austria

Organizer: Bjorn SandstedeBrown University, USA

8:00-8:25 Noise Induced State Transitions, Intermittency and Universality in the Noisy Kuramoto-Sivashinsky EquationGreg Pavliotis, Imperial College London,

United Kingdom

8:30-8:55 Not Available at Time of PublicationGabriel J. Lord, Heriot-Watt University,

United Kingdom

9:00-9:25 Interfaces in a Random EnvironmentNicolas Dirr, Cardiff University, United

Kingdom

9:30-9:55 Stability of Traveling Waves in Bistable Reaction-Diffusion EquationsWilhelm Stannat, Technische Universität

Berlin, Germany


Monday, August 11

CP1Internal Waves and Related Problems8:00 AM-10:00 AMRoom:Tizard Room - Concourse (1st Floor)

Chair: Paolo Luzzatto-Fegiz, University of Cambridge, United Kingdom

8:00-8:15 Internal Waves Incident Upon An InterfaceJohn P. Mchugh, University of New

Hampshire, USA

8:20-8:35 Laboratory Experiments and Simulations for Solitary Internal Waves with Trapped CoresPaolo Luzzatto-Fegiz, University of

Cambridge, United Kingdom; Karl Helfrich, Woods Hole Oceanographic Institute, USA

8:40-8:55 Mcc Type Strongly Nonlinear Internal Wave ModelsTae-Chang Jo, Inha University, Korea

9:00-9:15 Nonlinear Harmonic Generation by Internal Wave RefractionScott E. Wunsch, Johns Hopkins

University, USA

9:20-9:35 Cylindrical Korteweg-De Vries Type Equation for Internal and Surface Ring Waves on a Shear FlowXizheng Zhang and Karima

Khusnutdinova, Loughborough University, United Kingdom

9:40-9:55 The Rogue Wave Solutions of the KpiJingsong He, Ningbo University, China

Coffee Break10:00 AM-10:30 AMRoom:Concourse/Buttery (Ground Floor)

Monday, August 11

MS7Differential Geometry and Lie Groups in Continuum Modelling8:00 AM-10:00 AMRoom:Cockcroft Room - Concourse (Ground Floor)

Many continuum field theories such as fluids and solids have differential geometric descriptions. For example, in-viscid in-compressible fluid equations were characterized by V.I. Arnold as right trivialized geodesic equations on the psuedo-Lie group of volume preserving diffeomorphisms. In this minisymposium we will discuss examples of computational and analytical models which benefit from these geometric descriptions.

Organizer: Henry O. JacobsImperial College London, United Kingdom

8:00-8:25 Geometric Theory of Garden Hose DynamicsVakhtang Putkaradze, University of

Alberta, Canada

8:30-8:55 Using Multi-Moment Vortex Methods to Study MergerDavid T. Uminsky, University of San

Francisco, USA

9:00-9:25 Structure-preserving Discretization of Fluid MechanicsDmitry Pavlov, Imperial College London,

United Kingdom

9:30-9:55 Jet-Particle Methods for Incompressible FluidsColin Cotter, Imperial College London,

United Kingdom; Darryl D. Holm, Imperial College London, United Kingdom and Los Alamos National Laboratory, USA; Henry Jacobs, Imperial College London, United Kingdom

Monday, August 11

MS8Enhanced Dissipation in Fluids8:00 AM-10:00 AMRoom:JCR Games Room – Concourse (Ground Floor)

Typically, in fluid models, one main source of dissipation is the viscosity. However, there are many examples of fluid models in which temporal decay occurs at a much faster rate than one would expect on the basis of viscous effects alone. Recently mathematical and physical explanations of this enhanced dissipation have been proposed in a number of settings including weakly viscous vortices, strongly sheared flows, and Landau damping. This minisymposium will bring together speakers working on each of these problems to explore similarities and differences between the dissipation mechanism in each of these cases.

Organizer: Margaret BeckBoston University, USA

Organizer: C. Eugene WayneBoston University, USA

8:00-8:25 Inviscid Damping and the Asymptotic Stability of Planar Shear Flows in the 2D Euler EquationsJacob Bedrossian, Courant Institute

of Mathematical Sciences, New York University, USA

8:30-8:55 Large Deviations for Stochastic Partial Differential Equations with Applications in Planetary Atmosphere DynamicsFreddy Bouchet, ENS Lyon, France

9:00-9:25 Center Manifolds and Taylor DispersonOsman Chaudhary, Boston University,

USA

9:30-9:55 Pseudospectrum for Oseen Vortices OperatorsWen Deng, Lund University, Sweden


Monday, August 11Welcoming Remarks10:30 AM-10:45 AMRoom:Wolfson Auditorium - Wolfson Hall

IP1Stability and Synchrony in the Kuramoto Model10:45 AM-11:30 AMRoom:Wolfson Auditorium - Wolfson Hall

Chair:Jianke Yang, University of Vermont, USA

The phenomenon of the synchronization of weakly coupled oscillators is a old one, first been described by Huygens in his 'Horoloquium Oscilatorium.' Some other examples from science and engineering include the cardiac pacemaker, the instability in the Millenium Bridge, and the synchronous flashing of fireflies. A canonical model is the Kuramoto model

We describe the fully synchronized states of this model together with the dimensions of their unstable manifolds. Along the way we will encounter a high dimensional polytope, a Coxeter group, and a curious combinatorial identity. This leads to a proof of the existence of a phase transition in the case where the frequencies are chosen from as iid Random variables.

Jared BronskiUniversity of Illinois at Urbana-Champaign, USA

Lunch Break11:30 AM-1:00 PMAttendees on their own.

Meals will be available for purchase in the Dining Hall or Buttery snack bar.

Monday, August 11

IP2Integrability: Initial- Boundary Value Problems in 1+1, and Solitons in 3+11:00 PM-1:45 PMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Beatrice Pelloni, Uniersity of Reading, United Kingdom

A review will be presented of the two most challenging problems in the analysis of integrable nonlinear evolution equations: (a) initial- boundary value problems in 1+1, i.e. evolution equations in one spatial variable, and (b) the construction and solution of equations in 3+1. Regarding (a), it will be shown that the so- called unified transform, which provides the proper generalization of the inverse scattering transform, yields effective formulae for the large t- asymptotics of a variety of physically significant problems; this includes problems on the half-line with t-periodic boundary conditions. Regarding (b), an integrable generalization of the Davey-Stewardson equation 4+2, i.e. four spatial and two time variables, will be presented. A reduction of this equation to an equation in 3+1 will also be discussed. Furthermore, one and two soliton solutions for both the 4+2 and 3+1 Davey-Stewardson equations will be presented.

Thanasis FokasUniversity of Cambridge, United Kingdom

Intermission1:45 PM-2:00 PM

Monday, August 11

MS9Boundary-value Problems for Linear and Nonlinear Integrable Problems - Part II of III2:00 PM-4:00 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 1 see MS1 For Part 3 see MS17 In the last decade the use of a new method for solving boundary value problems due to Fokas has been expanded by him, his collaborators, and others. This method contains the classical solution methods as special cases and allows for the explicit solution of problems which could not previously be solved. This session will bring together practitioners of the Fokas Method and expose interested parties to the many applications of this technique.



2:00-2:25 Well-Posedness and Spectral Representation of Linear Initial-Boundary Value ProblemsDavid Smith, University of Crete, Greece

2:30-2:55 A Retrospective Inverse Problem for the Wave EquationVishal Vasan, Pennsylvania State University,

USA

3:00-3:25 Mixed Boundary Value Problems for Stokes Flows: New Methods and ApplicationsDarren G. Crowdy, Imperial College

London, United Kingdom

3:30-3:55 The Nonlinear Schrödinger Equation with Periodic Boundary DataJonatan Lenells, Baylor University, USA


Monday, August 11

MS12Nonlinear Dynamics of Granular Crystals - Part II of II2:00 PM-4:00 PMRoom:Recital Room - Music Center

For Part 1 see MS4 Granular crystals are defined as ordered aggregates of elastically interacting particles. They can be assembled as homogeneous, heterogeneous, one-dimensional or even higher dimensional structures and can be tailored to have tunable nonlinear responses. This tunability makes granular crystals relevant for a host of engineering applications, including e.g. shock absorbing layers, acoustic lenses and sound scramblers. In that light, and in connection also to the plenary talk by Professor Chiara Daraio, the aim of this minisymposium is to bring together researchers studying problems in this field with view points from application, experiment, computation and analysis.

Organizer: Christopher ChongUniversity of Massachusetts, Amherst, USA

Organizer: Miguel MoleronETH Zürich, Switzerland

2:00-2:25 Disordered Granular ChainsMason A. Porter, University of Oxford,

United Kingdom

2:30-2:55 Modulation of Nonlinear Waves in Woodpile Phononic CrystalsJinkyu Yang and Eunho Kim, University

of Washington, USA

3:00-3:25 Granular Crystals at the MicroscaleNicholas Boechler, University of

Washington, USA

3:30-3:55 Solitary Waves in a 1D Chain of Repelling MagnetsMiguel Moleron, ETH Zürich,

Switzerland; Andrea Leonard, University of Washington, USA; Chiara Daraio, ETH Zürich, Switzerland and California Institute of Technology, USA

Monday, August 11

MS10Modeling and Prediction of Geophysical Flows - Part I of II2:00 PM-4:00 PMRoom:Jock Colville Hall - Archives Center

For Part 2 see MS18 This set of presentations addresses waves, coherent structures, instabilities and turbulence in a variety of geophysical settings. A central goal is to isolate dynamical mechanisms fundamental for modeling and prediction in applications.

Organizer: Leslie SmithUniversity of Wisconsin, USA

2:00-2:25 A Coupled Model of the Interactions Between Inertial Waves and Turbulence in the OceanJacques Vanneste and Jin-Han Xie,

University of Edinburgh, United Kingdom

2:30-2:55 Not Available at Time of PublicationJean-Marc Chomaz, Ecole Polytechnique,

France

3:00-3:25 Centrifugal, Barotropic and Baroclinic Instabilities of Isolated Ageostrophic Anticyclones in the Two-layer Rotating Shallow Water Model and their Nonlinear SaturationVladimir Zeitlin, ENS/University of Paris

6, France; Noé Lahaye, University of Paris VI, France

3:30-3:55 Dissection of Boussinesq Non-linear Interactions Using Intermediate ModelsGerardo Hernandez-Duenas, University of

Wisconsin, Madison, USA; Leslie Smith, University of Wisconsin, USA; Samuel Stechmann, University of Wisconsin, Madison, USA

Monday, August 11

MS11Large Time Behavior in Schrödinger Equations from Different Perspectives - Part II of III2:00 PM-4:00 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 1 see MS3 For Part 3 see MS19 Partial differential equations of linear and/or nonlinear Schrödinger type furnish a canonical description of wave propagation in dispersive media. These equations have numerous applications, ranging from quantum mechanics, fiber optics, plasma physics and the description of water waves. One of the most important problems in the mathematical analysis of these equations concerns the precise description of solutions over long times. The proposed minisymposium will bring together experts in the analysis of Schrödinger equations who will give an overview of the current state-of-the art of the mathematical theory invoking several different perspectives, such as stochastics, geometry, and high frequency analysis.



2:00-2:25 Selection Principles for Semiclassical Flows over Conical Singularities: Asymptotic and Computational InvestigationAgisilaos Athanassoulis, University of

Leicester, United Kingdom

2:30-2:55 Nonlinear Propagation of Coherent States Through Avoided Energy Level CrossingLysianne Hari, Universite de Cergy-Pontoise,

France

3:00-3:25 Dispersion and Long Time Evolution of Coherent StatesRoman Schubert, University of Bristol,

United Kingdom

3:30-3:55 Dispersive Estimates for Non-Autonomous Hamiltonians and Applications to Nonlinear Asymptotic Stability of Solitary WavesEduard Kirr, University of Illinois at Urbana-

Champaign, USA


Monday, August 11

MS13Spectral and Geometric Methods in Stability of Waves and Patterns - Part I of V2:00 PM-4:00 PMRoom:Club Room - Concourse (1st Floor)

For Part 2 see MS21 The purpose of this session is to bring together researchers working on various stability issues for such special solutions of partial differential equations as patterns and waves. All aspects of stability/instability will be discussed, from spectral to nonlinear, with special emphasis on methods of spectral theory. It is expected that the speakers will spend some time of their talks to address possible perspectives in the field of their work as we believe that such a perspective would be not only interesting for the audience but it can also stimulate further discussion and further research in the field.

Organizer: Anna GhazaryanMiami University and University of Kansas, USA

Organizer: Yuri LatushkinUniversity of Missouri, Columbia, USA

2:00-2:25 On the Maslov Index for Periodic and for Multidimensional ProblemsYuri Latushkin, University of Missouri,

Columbia, USA

2:30-2:55 Computing the Maslov IndexSimon Malham, Heriot-Watt University,

United Kingdom; Margaret Beck, Boston University, USA

3:00-3:25 The Krein Matrix for Quadratic Eigenvalue ProblemsTodd Kapitula, Shamuel Auyeung, and

Eric Yu, Calvin College, USA

3:30-3:55 Determining Wave Stability Via the Maslov IndexGraham Cox, Chris Jones, and Jeremy L.

Marzuola, University of North Carolina, Chapel Hill, USA

Monday, August 11

MS14Pattern Formation and Evolving Domains2:00 PM-4:00 PMRoom:Bevin Room - Wolfson Hall

The application of the theory of pattern formation to realistic situations is often constrained by the non-constant nature of the environment, in particular the shape of the domain. However, the pattern formation theory for this context is not yet well developed. In this minisymposium, we bring together researchers with different perspectives on this topic, ranging from modeling, PDE theory and numerics to existence and stability. Evolving domains are seen to be a source of both new, intriguing phenomena and challenging mathematics. Applications cover in particular chemistry (binary gas/liquid mixtures) and biology (evolving tissue, cell motility).

Organizer: Frits VeermanUniversity of Oxford, United Kingdom

Organizer: Jens RademacherUniversity of Bremen, Germany

2:00-2:25 Spatial Patterns on Time-Dependent Domains: Convective and Dilution EffectsRouslan Krechetnikov, University of

California, Santa Barbara, USA; Edgar Knobloch, University of California, Berkeley, USA

2:30-2:55 Recent Advances in Pattern Formation on Growing and Evolving Surfaces: Theory, Numerics and ApplicationsAnotida Madzvamuse, University of

Sussex, United Kingdom

3:00-3:25 Modelling and Simulation of Biological Pattern Formation on Evolving SurfacesChandrashekar Venkataraman, University

of Sussex, United Kingdom

3:30-3:55 Effect of Dissolution-Driven Convection on the Partial Mixing Between CO2 and Hydrocarbons Or Reactive SolutionsLaurence Rongy, Université Libre de

Bruxelles, Belgium

Monday, August 11

MS15Integrable Systems: Analysis, Geometry, and Applications - Part I of II2:00 PM-4:00 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 2 see MS23 The minisymposium brings together specialists studying nonlinear waves in integrable evolution equations. The particular emphasis will be given to recent analytical studies of Backlund transformation, inverse scattering, and conserved quantities in the context of global well-posedness of the Cauchy problem, as well as orbital and asymptotic stability of breathers and solitons, including multi-solitons. From another direction, recent work in geometry of integrable systems has led to new sources of analytical problems arising from geodesic flows in circle diffeomorphism groups and inelastic curve flows in Klein geometries. These problems involve the study of periodic peakons and multi-component peakons, as well as multi-component solitons.

Organizer: Stephen AncoBrock University, Canada

Organizer: Dmitry PelinovskyMcMaster University, Canada

2:00-2:25 Stability of mKdV Breathers in the Energy SpaceMiguel Alejo, IMPA, Brazil

2:30-2:55 On the Interaction of Nonlinear Schödinger Solitary WavesClaudio Munoz, University of Paris, Orsay,

France

3:00-3:25 Stability of Line Standing Waves Near the Bifurcation Point for Nonlinear Schrodinger EquationYohei Yamazaki, Kyoto University, Japan

3:30-3:55 On the Dressing Method for Discrete Integrable SystemsQiao Wang, and Gino Biondini, State

University of New York, Buffalo, USA


Monday, August 11

MS16Coherent Structures in Nonlocal Evolution Equations - Part I of II2:00 PM-4:00 PMRoom:JCR Games Room – Concourse (Ground Floor)

For Part 2 see MS24 The aim of this minisymposium is to present an overview of some recent and novel analytical techniques developed in the study of coherent structures in nonlocal evolution equations. Talks will range from lattice ODEs over fluid problems to nonlocal reaction-diffusion, all sharing the common feature that nonlocal terms are involved and pose particular mathematical difficulties.

Organizer: Gregory FayeUniversity of Minnesota, USA

Organizer: Arnd ScheelUniversity of Minnesota, USA

2:00-2:25 Waves Through Lattices with ImpuritiesHermen Jan Hupkes, University of Leiden,

The Netherlands; Aaron Hoffman, Franklin W. Olin College of Engineering, USA; Erik Van Vleck, University of Kansas, USA

2:30-2:55 Using Graph Limits for Studying Dynamics of Large NetworksGeorgi S. Medvedev, Drexel University,

USA

3:00-3:25 Phase Mixing and Hydrodynamic StabilityJacob Bedrossian, Courant Institute


3:30-3:55 Reaction-Diffusion Equations with Spatially Distributed HysteresisPavel Gurevich, Free University of Berlin,

Germany

Monday, August 11

MS17Boundary-value Problems for Linear and Nonlinear Integrable Problems - Part III of III4:30 PM-6:00 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS9 In the last decade the use of a new method for solving boundary value problems due to Fokas has been expanded by him, his collaborators, and others. This method contains the classical solution methods as special cases and allows for the explicit solution of problems which could not previously be solved. This session will bring together practitioners of the Fokas Method and expose interested parties to the many applications of this technique.



4:30-4:55 A New Approach for Linear Elliptic Boundary Value ProblemsAnthony Ashton, University of


5:00-5:25 Initial-Boundary-Value Problems for Nonlinear Wave EquationsJerry Bona, University of Illinois,

Chicago, USA

5:30-5:55 The Effect of Boundary Conditions on Linear and Nonlinear WavesBeatrice Pelloni, University of Reading,

United Kingdom

Monday, August 11

CP2Integrability and Related Problems2:00 PM-3:20 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Alfredo N. Wetzel, University of Michigan, Ann Arbor, USA

2:00-2:15 Boundary Value Problems for Multidimensional Integrable Nonlinear PdesIasonas Hitzazis, University of Patras,

Greece

2:20-2:35 Variable Separation Solutions and Interacting Waves of a Coupled System of the Modified KdV and Potential Blmp EquationsXiaoyan Tang, East China Normal

University, China; Ji Lin, Zhejiang Normal University, China; Zufeng Liang, Hangzhou Normal University, China

2:40-2:55 Explicit Construction of the Direct Scattering Transform for the Benjamin-Ono Equation with Rational Initial ConditionsAlfredo N. Wetzel and Peter D. Miller,

University of Michigan, Ann Arbor, USA

3:00-3:15 Model Order Reduction for Coupled Nonlinear Schrödinger EquationCanan Akkoyunlu, Istanbul Kültür

University, Turkey; Murat Uzunca and Bülent Karasözen, Middle East Technical University, Turkey

Coffee Break4:00 PM-4:30 PMRoom:Concourse/Buttery (Ground Floor)


Monday, August 11

MS18Modeling and Prediction of Geophysical Flows - Part II of II4:30 PM-6:30 PMRoom:Jock Colville Hall - Archives Center

For Part 1 see MS10 This set of presentations addresses waves, coherent structures, instabilities and turbulence in a variety of geophysical settings. A central goal is to isolate dynamical mechanisms fundamental for modeling and prediction in applications.

Organizer: Leslie SmithUniversity of Wisconsin, USA

4:30-4:55 On Resurging a Bore-Soliton-SpashOnno Bokhove, University of Leeds,

United Kingdom

5:00-5:25 A Dynamical Scheme for Prescribing Mesoscale Eddy Diffusivity in the OceanScott Bachman, University of Cambridge,

United Kingdom; Baylor Fox-Kemper, Brown University, USA

5:30-5:55 Cloud-Edge Dynamics and Mysterious Holes in the SkyDavid Muraki, Simon Fraser University,

Canada

6:00-6:25 A Strange Gas? Revisiting the Point Vortex Model to Understand the Condensation Process in Two-Dimensional and Quasi-Geostrophic TurbulenceGavin Esler, University College London,

United Kingdom

Monday, August 11

MS20Modeling of Optical Combs and Low-Noise Opto-Electronic Sources - Part I of III4:30 PM-6:30 PMRoom:Recital Room - Music Center

For Part 2 see MS28 In the past decade, new optical devices have been invented and old ones have been refined, leading to a dramatic decrease in the noise floor of time and frequency transfer devices. The devices include opto-electronic oscillators, comb lasers, microresonators, and narrow-linewidth continuous wave lasers. The range of applications is vast and includes astrophysics, telecommunications, medicine, and radio-frequency photonics. The modeling of these devices has not kept pace wit these experimental advances, which have opened up new theoretical problems that are related to solitons and nonlinear dynamics. In this minisymposium, we will highlight recent advances in modeling these devices and point to the new mathematical problems that they have opened.

Organizer: Omri GatHebrew University of Jerusalem, Israel

Organizer: Curtis R. MenyukUniversity of Maryland, Baltimore County, USA

Organizer: Stefan WabnitzUniversity of Brescia, Italy

4:30-4:55 From Microresonator Combs to SolitonsMichael Gorodetsky, Lomonosov Moscow

State University, Russia

5:00-5:25 Kerr Optical Frequency Combs: from Fundamental Theory to Engineering ApplicationsYanne Chembo, FEMTO-ST Institute, France

Monday, August 11

MS19Large Time Behavior in Schrödinger Equations from Different Perspectives - Part III of III4:30 PM-6:30 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS11 Partial differential equations of linear and/or nonlinear Schrödinger type furnish a canonical description of wave propagation in dispersive media. These equations have numerous applications, ranging from quantum mechanics, fiber optics, plasma physics and the description of water waves. One of the most important problems in the mathematical analysis of these equations concerns the precise description of solutions over long times. The proposed minisymposium will bring together experts in the analysis of Schrödinger equations who will give an overview of the current state-of-the art of the mathematical theory invoking several different perspectives, such as stochastics, geometry, and high frequency analysis.



4:30-4:55 Dispersive Blow-Up in Schrödinger Type EquationsChristof Sparber, University of Illinois,

Chicago, USA

5:00-5:25 Invariant Gibbs Measures for NLS on the Real LineTadahiro Oh, University of Edinburgh,

United Kingdom

5:30-5:55 Two-soliton Solutions to a Focusing Cubic Half-wave Equation on ROana Pocovnicu, Princeton University, USA

6:00-6:25 Going Beyond the Threshold: Scattering vs. Blow-up Dichotomy in the Focusing NLS Equation Svetlana Roudenko, George Washington University, USA



Monday, August 11

MS22Patterns in Many-body Collective Motion4:30 PM-6:30 PMRoom:Bevin Room - Wolfson Hall

Patterns in many-body dynamics -- as seen in traffic flow, broadly defined as collections of cars or people, and in aggregation equations, used to model biological “swarms” of bacteria and chemical self-assembly -- are ubiquitous in the natural world. These phenomena are generally studied numerically, but some cases, such as the aggregation equations, have recently become analytically tractable, usually through studying an associated continuum limit of a discrete particle model. This minisymposium brings together researchers from a diverse set of problems all related to the study of patterns arising from many-body interactions on computational, analytical, and experimental levels.

Organizer: Scott McCallaUniversity of California, Los Angeles, USA

Organizer: Martin ShortGeorgia Institute of Technology, USA

4:30-4:55 Contagion Shocks in One DimensionMartin Short, Georgia Institute of

Technology, USA; Andrea L. Bertozzi, Li Wang, and Jesus Rosado, University of California, Los Angeles, USA

5:00-5:25 Agent-Based and Continuum Models for the Formation of Stripes in ZebrafishAlexandria Volkening and Bjorn

Sandstede, Brown University, USA

5:30-5:55 Co-Dimension One Self-AssemblyJames von Brecht, University of

California, Los Angeles, USA

6:00-6:25 Front Propagation in Bacterial SuspensionsRay E. Goldstein, University of


5:30-5:55 Modelocking Quantum Cascade Lasers Using Quantum Coherent Saturable AbsorptionMuhammad Talukder, Bangladesh

University of Engineering & Technology, Bangladesh; Curtis R. Menyuk, University of Maryland, Baltimore County, USA

6:00-6:25 Pulse Energy Enhancement of Mode Locked Fiber Laser by Cascading Nonlinear Polarization RotationFeng Li, Hong Kong Polytechnic University,

China; J. Nathan Kutz, University of Washington, USA; P. K. Alex Wai, Hong Kong Polytechnic University, China

Monday, August 11

MS21Spectral and Geometric Methods in Stability of Waves and Patterns - Part II of V4:30 PM-6:30 PMRoom:Club Room - Concourse (1st Floor)

For Part 1 see MS13 For Part 3 see MS29 The purpose of this session is to bring together researchers working on various stability issues for such special solutions of partial differential equations as patterns and waves. All aspects of stability/instability will be discussed, from spectral to nonlinear, with special emphasis on methods of spectral theory. It is expected that the speakers will spend some time of their talks to address possible perspectives in the field of their work as we believe that such a perspective would be not only interesting for the audience but it can also stimulate further discussion and further research in the field.



4:30-4:55 Stability of Fronts in Spatially Inhomogeneous Wave EquationsGianne Derks and Christopher Knight,

University of Surrey, United Kingdom; Arjen Doelman, Leiden University, Netherlands; Hadi Susanto, University of Essex, United Kingdom

5:00-5:25 Spectral Analysis for Transition Front Solutions in Multidimensional Cahn-Hilliard SystemsPeter Howard, Texas A&M University,

USA

5:30-5:55 Stability and Computation of Interacting Nonlinear WavesWolf-Juergen Beyn, Bielefeld University,

Germany

6:00-6:25 A Geometric Approach to Counting Eigenvalues: The Evans Function in Some Cellular Transport ModelsRobert Marangell, University of Sydney,

Australia


Monday, August 11

MS24Coherent Structures in Nonlocal Evolution Equations - Part II of II4:30 PM-6:30 PMRoom:JCR Games Room – Concourse (Ground Floor)

For Part 1 see MS16 The aim of this minisymposium is to present an overview of some recent and novel analytical techniques developed in the study of coherent structures in nonlocal evolution equations. Talks will range from lattice ODEs over fluid problems to nonlocal reaction-diffusion, all sharing the common feature that nonlocal terms are involved and pose particular mathematical difficulties.

Organizer: Gregory FayeUniversity of Minnesota, USA

Organizer: Arnd ScheelUniversity of Minnesota, USA

4:30-4:55 From Particle to Kinetic and Hydrodynamic Models of FlockingTrygve K. Karper, Norwegian University of

Science and Technology, Norway

5:00-5:25 A Spectral Theory of Linear Operators on a Gelfand Triplet and Its Application to the Dynamics of Coupled OscillatorsHayato Chiba, Kyushu University, Japan

5:30-5:55 Pacemakers in a Large Array of Oscillators with Nonlocal CouplingGabriela Jaramillo, University of

Minnesota, USA

6:00-6:25 A Tale of Two Distributions: from Few to Many Vortices In Quasi-Two-Dimensional Bose-Einstein CondensatesTheodore Kolokolnikov, Dalhousie

University, Canada; Panayotis Kevrekidis, University of Massachusetts, Amherst, USA; Ricardo Carretero, San Diego State University, USA

Monday, August 11

CP3Solitary Waves and Related Problems4:30 PM-6:30 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: John P. Boyd, University of Michigan, Ann Arbor, USA

4:30-4:45 Resonance, Small Divisors and the Convergence of Newton’s Iteration to SolitonsJohn P. Boyd, University of Michigan, Ann

Arbor, USA

4:50-5:05 Solitary Wave Perturbation Theory for Hamiltonian SystemsLake Bookman and Mark A. Hoefer, North

Carolina State University, USA

5:10-5:25 Orbital Stability of Solitary Shallow Water Waves of Moderate AmplitudeAnna Geyer, Universitat Autònoma de

Barcelona, Spain; Nilay Duruk Mutlubas, Kemerburgaz University, Istanbul, Turkey

5:30-5:45 Velocity Field in Parametrically Excited Solitary WavesLeonardo Gordillo, Universite Paris

7-Denis Diderot, France; Nicolas Mujica, Universidad de Chile, Chile

5:50-6:05 Solitary Waves and an N-particle Algorithm for a Class of Euler-Poincaré EquationsLong Lee, University of Wyoming, USA;

Roberto Camassa, University of North Carolina, Chapel Hill, USA; Dongyang Kuang, University of Wyoming, USA

6:10-6:25 The (1+2)-Dimensional Sine-Gordon Equation: Soliton Solutions and Spatially Extended Relativistic ParticlesYair Zarmi, Ben-Gurion University of the

Negev, Israel

Dinner Break6:30 PM-8:00 PMAttendees on their own. Meals will be available for purchase in the Dining Hall or Buttery snack bar.

Martin D. Kruskal Prize Presentation8:00 PM-8:15 PMRoom:Wolfson Auditorium - Wolfson Hall

Monday, August 11

MS23Integrable Systems: Analysis, Geometry, and Applications - Part II of II4:30 PM-6:30 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 1 see MS15 The minisymposium brings together specialists studying nonlinear waves in integrable evolution equations. The particular emphasis will be given to recent analytical studies of Backlund transformation, inverse scattering, and conserved quantities in the context of global well-posedness of the Cauchy problem, as well as orbital and asymptotic stability of breathers and solitons, including multi-solitons. From another direction, recent work in geometry of integrable systems has led to new sources of analytical problems arising from geodesic flows in circle diffeomorphism groups and inelastic curve flows in Klein geometries. These problems involve the study of periodic peakons and multi-component peakons, as well as multi-component solitons.

Organizer: Stephen AncoBrock University, Canada

Organizer: Dmitry PelinovskyMcMaster University, Canada

4:30-4:55 The Analysis of a Class of Integrable Evolution EquationsAlex Himonas, University of Notre Dame,

USA

5:00-5:25 Integrable Equations in 3D: Deformations of Dispersionless LimitsVladimir Novikov, Loughborough


5:30-5:55 Well Posedness and Breakdown for Cauchy Problems of Integrable EquationsFeride Tiglay, The Ohio State University,

USA

6:00-6:25 Geometric Wave Equations with Multi-component SolitonsStephen Anco, Brock University, Canada


Monday, August 11

SP1Martin D. Kruskal Prize Lecture - Nonlinear Waves from Beaches to Photonics8:15 PM-9:00 PMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Edgar Knobloch, University of California, Berkeley, USA

Based on work of Kruskal et al the Korteweg-deVries equation was found to have many remarkable properties. These properties are shared by many other equations including the 2D Kadomtsev-Petvishvili (KP) equation, which arises in the study of shallow water waves. Some solutions of KP and their relation to waves on shallow beaches will be discussed. Nonlinear waves in photonic periodic lattices will also be described; “photonic graphene” is a remarkable case. Since this is an evening lecture, equations and details will be kept to a minimum, and the lecture will be colloquium style.

Mark Ablowitz, University of Colorado, USA

Tuesday, August 12


MS25Inverse Scattering Transform and Riemann--Hilbert Problems - Part I of III8:10 AM-10:10 AMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS32 Since the inverse scattering transform was introduced to linearize integrable nonlinear PDEs, a large body of knowledge has been accumulated on these systems. Riemann-Hilbert problems (RHPs) have proven to be a powerful tool for the study of integrable systems [e.g., in the formulation of the inverse problem and for asymptotic analysis of the solutions], and found many connections to other areas of pure and applied mathematics. The session aims at bringing together leading researchers in these areas, and at offering a broad overview of some of the current research activities at the frontier of pure and applied mathematics.

Organizer: Barbara PrinariUniversity of Colorado, Colorado Springs, USA

Organizer: Gino BiondiniState University of New York, Buffalo, USA

8:10-8:35 The Unified Transform and the Riemann-Hilbert FormalismAthanassios S. Fokas, University of


8:40-9:05 A Coupling Problem for Entire Functions and Its Application to the Long-Time Asymptotics of Integrable Wave EquationsGerald Teschl, University of Vienna,

Austria; Jonathan Eckhardt, Cardiff University, United Kingdom

9:10-9:35 A Riemann-Hilbert Approach for the Degasperis-Procesi and Ostrovsky-Vakhnenko EquationsAnne Boutet de Monvel, Universite Paris

VI, France

9:40-10:05 Long-Time Asymptotics for the Toda Shock ProblemJohanna Michor and Gerald Teschl,

University of Vienna, Austria; Iryna Egorova, National Academy of Science, Ukraine

continued in next column


Tuesday, August 12

MS28Modeling of Optical Combs and Low-Noise Opto-Electronic Sources - Part II of III8:10 AM-10:10 AMRoom:Recital Room - Music Center

For Part 1 see MS20 For Part 3 see MS35 In the past decade, new optical devices have been invented and old ones have been refined, leading to a dramatic decrease in the noise floor of time and frequency transfer devices. The devices include opto-electronic oscillators, comb lasers, microresonators, and narrow-linewidth continuous wave lasers. The range of applications is vast and includes astrophysics, telecommunications, medicine, and radio-frequency photonics. The modeling of these devices has not kept pace wit these experimental advances, which have opened up new theoretical problems that are related to solitons and nonlinear dynamics. In this minisymposium, we will highlight recent advances in modeling these devices and point to the new mathematical problems that they have opened.




8:10-8:35 Tunable Photonic OscillatorsVassilios Kovanis, Virginia Tech, USA

8:40-9:05 Dynamics of Frequency Comb Generation and Design of Planar Microring ResonatorsTobias Hansson, Daniele Modotto, and

Stefan Wabnitz, University of Brescia, Italy

9:10-9:35 Azimuthal Dissipative Structures in Whispering-Gallery Mode ResonatorsAurelien Coillet, FEMTO-ST Institute,

France

9:40-10:05 Injection Locking of Frequency Combs in Mode Locked LasersOmri Gat, Hebrew University of Jerusalem,

Israel; David Kielpinski, Griffith University, Brisbane, Australia

Tuesday, August 12

MS27Solitary Waves in Inhomogeneous Structures - Part I of III8:10 AM-10:10 AMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS34 The goal of the minisymposium is to discuss different aspects of Solitary waves (SW) in inhomogeneous structures, from analytical, numerical as well as applied points of view. On the one hand, there are results on the existence of SW in periodic media, e.g. asymptotics via envelope approximations and ground state solutions, and on wave propagation in media with variable (not necessarily periodic) coefficients. More recently, scattering of SW from strongly localized perturbations, e.g., delta potentials on the line or vertices in graphs has been studied. Important applications include dispersion management, waves at interfaces, in photonic crystals, waveguide arrays, and in networks.

Organizer: Tomas DohnalTechnische Universität Dortmund, Germany

Organizer: Hannes UeckerUniversity of Oldenburg, Germany

8:10-8:35 Movement of Gap Solitons across Deep Gratings in the Periodic NLSTomas Dohnal, Technische Universität

Dortmund, Germany

8:40-9:05 Periodic and Relative Periodic Solutions in a Multiple Waveguide SystemRoy Goodman, New Jersey Institute of

Technology, USA

9:10-9:35 Solitary Wave Dynamics in Plasmonic Binary ArraysAlejandro Aceves, Southern Methodist

University, USA; Costantino De Angelis, Aldo Auditore, and Matteo Conforti, University of Brescia, Italy

9:40-10:05 Stochasticity and Coherent Structures in Ultra-Long Mode-Locked LasersDmitry Churkin, Aston University, United

Kingdom

Tuesday, August 12

MS26Nonlinear Waves in Geophysical Fluid Dynamics - Part I of III8:10 AM-10:10 AMRoom:Jock Colville Hall - Archives Center

For Part 2 see MS33 Nonlinear waves pervade GFD from classical water waves to internal atmospheric and oceanic waves. The minisymposium brings together some recent modelling and results in this broad field.

Organizer: Paul A. MilewskiUniversity of Bath, United Kingdom

Organizer: Andre NachbinInstitute of Pure and Applied Mathematics, Brazil

8:10-8:35 Particle Trajectories Beneath Stokes’ WavesPaul A. Milewski, University of Bath,

United Kingdom; Andre Nachbin, Institute of Pure and Applied Mathematics, Brazil; Roberto Ribeiro-Junior, IMPA, Brazil

8:40-9:05 Diapycnal Mixing and Overturning CirculationsEsteban G. Tabak, Courant Institute


9:10-9:35 Effective Boundary Conditions for Semi-Open Dispersive SystemsRodolfo R. Rosales, Massachusetts

Institute of Technology, USA; Lyubov Chumakova, University of Edinburgh, United Kingdom; Esteban G. Tabak, Courant Institute of Mathematical Sciences, New York University, USA

9:40-10:05 Effective Boundary Conditions: An Application to the AtmosphereLyubov Chumakova, University of

Edinburgh, United Kingdom; Rodolfo R. Rosales, Massachusetts Institute of Technology, USA; Esteban G. Tabak, Courant Institute of Mathematical Sciences, New York University, USA


Tuesday, August 12

MS31Vortex Dynamics of Superfluids8:10 AM-10:40 AMRoom:Cockcroft Room - Concourse (Ground Floor)

The session focuses on quantized superfluid vortices with a focus on the superfluid phase of liquid Helium. Consideration of the dynamics of vortices turns out to be crucial for a fundamental understanding of turbulent flows in the superfluid regime. The session will feature a range of talks describing numerical simulations based on vortex filament models as well as mean-field models based on the nonlinear Schrodinger equation. This is complemented by talks on analytical studies of soliton excitations on quantised vortices and experimental studies of vortex dynamics in liquid Helium providing a broad overview of the key developments in the field.

Organizer: Hayder SalmanUniversity of East Anglia, United Kingdom

8:10-8:35 Vortex Reconnections and Implications for Inverse Energy Transfer in Turbulent Superfluid HeliumCarlo F. Barenghi, Newcastle

University, United Kingdom; Andrew Baggaley, University of Glasgow, Scotland, United Kingdom; Yuri Sergeev, Newcastle University, United Kingdom

8:40-9:05 Breathers on Quantized Superfluid VorticesHayder Salman, University of East

Anglia, United Kingdom

9:10-9:35 Reconnections of Vortex Rings in Superfluid HeliumPaul Walmsley, P.M. Tompsett, D.E.

Zmeev, and A.I. Golov, University of Manchester, United Kingdom

9:40-10:05 Thermal Counterflow in a Periodic Channel with Solid BoundariesAndrew Baggaley, University of

Glasgow, Scotland, United Kingdom; Jason Laurie, Weizmann Institute of Science, Israel

10:10-10:35 Local and Nonlocal Effects in Quantum TurbulenceLucy Sherwin, Newcastle University,

United Kingdom

Tuesday, August 12

MS30Liquid Crystals: Beyond Display Applications8:10 AM-10:10 AMRoom:Bevin Room - Wolfson Hall

Liquid crystals (LCs) are intermediate or mesogenic phases of matter which combine liquid fluidity with crystalline solid properties. In recent years, LCs have revolutionized the display industry. LCs now have fundamentally new applications beyond displays, in materials science and biology. This minisymposium comprises four talks: Kralj will speak about novel defect-stabilized LC structures; Vitelli will address questions related to defects and curvature; Sengupta will describe exciting experimental work on LC microfluidics and Dawes will talk about smectic liquid crystals. Between themselves, the speakers cover a range of emerging interdisciplinary research fields with ample scope for new developments.

Organizer: Apala MajumdarUniversity of Bath, United Kingdom

8:10-8:35 Shear-induced Instability of a Smectic A Liquid CrystalJonathan Dawes, University of Bath,

United Kingdom; Iain W. Stewart, University of Strathclyde, United Kingdom

8:40-9:05 Frustrated Nematic Order in Spherical GeometriesVincenzo Vitelli, Universiteit Leiden, The

Netherlands

9:10-9:35 Imry-Ma-Larkin Clusters in Random NematicsSamo Kralj, University of Maribor,

Slovenia

9:40-10:05 Harnessing Topological Defects via Liquid Crystal MicrofluidicsAnupam Sengupta, Massachusetts

Institute of Technology, USA; Stephan Herminghaus and Christian Bahr, Max Planck Institute for Dynamics and Self-Organization, Germany

Tuesday, August 12

MS29Spectral and Geometric Methods in Stability of Waves and Patterns - Part III of V8:10 AM-10:10 AMRoom:Club Room - Concourse (1st Floor)




8:10-8:35 Transverse Dynamics of Periodic Gravity-Capillary Water WavesMariana Haragus, Université de Franche-

Comté, France; Erik Wahlen, Lund University, Sweden

8:40-9:05 Orbital Stability of Periodic Waves and Black Solitons in the Cubic Defocusing NLS EquationDmitry Pelinovsky, McMaster University,

Canada

9:10-9:35 Stability of Traveling Waves on Vortex FilamentsStephane Lafortune, Annalisa M. Calini, and

Scotty Keith, College of Charleston, USA

9:40-10:05 Stability of Viscous Roll-WavesMat Johnson, University of Kansas, USA;

Pascal Noble, University of Toulouse, France; Miguel Rodrigues, University of Lyon 1, France; Kevin Zumbrun and Blake Barker, Indiana University, USA


Tuesday, August 12Remarks10:40 AM-10:45 AMRoom:Wolfson Auditorium - Wolfson Hall

IP3Minimal Models for Precipitating Convection10:45 AM-11:30 AMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Paul A. Milewski, University of Bath, United Kingdom

Despite the importance of organized convection (e.g. squall lines and hurricanes), numerical simulations remain a challenge. Comprehensive cloud resolving models would include water vapor, liquid water and ice, and liquid water would be separated into cloud water and rain water. Here we take a minimalist approach to cloud microphysics by incorporating fast auto-conversion from cloud to rain water, and fast condensation and evaporation. Numerical and analytical results will be discussed, e.g., saturated regions have a linear stability boundary associated with parcel (finite-amplitude) stability in unsaturated regions.

Leslie SmithUniversity of Wisconsin, USA



Tuesday, August 12

CP5Mathematical Biology and Related Problems8:10 AM-10:10 AMRoom:Tizard Room - Concourse (1st Floor)

Chair: Sofia Piltz, University of Oxford, United Kingdom

8:10-8:25 Pipes and NeuronsDwight Barkley, University of Warwick,

United Kingdom; Baofang Song and Mukund Vasudevan, Institute of Science and Technology, Austria; Marc Avila, University of Erlangen-Nuremberg, Germany; Bjoern Hof, Institute of Science and Technology, Austria

8:30-8:45 Localized Structures and Their Dynamics in Bioconvection of Euglena GracilisMakoto Iima, Erika Shoji, Akinori Awazu,

Hiraku Nishimori, and Shunsuke Izumi, Hiroshima University, Japan

8:50-9:05 Models for Adaptive Feeding and Plankton PopulationsSofia Piltz, Mason A. Porter, and Philip

K. Maini, University of Oxford, United Kingdom

9:10-9:25 Self-Organisation in a Reaction-Diffusion System with a Non-Diffusing ComponentPeter Rashkov, Philipps-Universität,

Marburg, Germany

9:30-9:45 On a Volume-Surface Reaction-Diffusion System with Nonlinear Boundary Coupling: Well-Posedness and Exponential Convergence to EquilibriumBao Q. Tang, Klemens Fellner, and

Evangelos Latos, University of Graz, Austria

9:50-10:05 Optimal Control in a Mathematical Model of Low Grade GliomaJuan Belmonte-Beitia, Universidad de

Castilla-La Mancha, Spain


Tuesday, August 12

CP4Nonlinear Schrodinger Equations and Related Problems8:10 AM-9:30 AMRoom:JCR Games Room – Concourse (Ground Floor)

Chair: Justin Cole, Florida State University, USA

8:10-8:25 Spectral Band Gaps and Lattice Solitons for the Fourth Order Dispersive Nonlinear Schrödinger Equation with Time Periodic PotentialJustin Cole and Ziad Musslimani, Florida

State University, USA

8:30-8:45 Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger EquationHideshi Yamane, Kwansei Gakuin

University, Japan

8:50-9:05 Transverse Instability of a Soliton Solution to Quadratic Nonlinear Schrödinger EquationSarun Phibanchon, Mahidol University

and Burapha University, Thailand; Michael Allen, Mahidol University, Thailand

9:10-9:25 On Rational Solutions to Multicomponent Nonlinear Derivative Schrödinger EquationTihomir I. Valchev, Dublin Institute of

Technology, Ireland


Tuesday, August 12

MS33Nonlinear Waves in Geophysical Fluid Dynamics - Part II of III2:00 PM-3:30 PMRoom:Jock Colville Hall - Archives Center

For Part 1 see MS26 For Part 3 see MS41 Nonlinear waves pervade GFD from classical water waves to internal atmospheric and oceanic waves. The minisymposium brings together some recent modelling and results in this broad field.



2:00-2:25 Breaking of Interfacial Waves Induced by Background RotationTed Johnson, University College London,

United Kingdom

2:30-2:55 Pure Gravity Generalised Solitary WavesJean-Marc Vanden-Broeck, University

College London, United Kingdom

3:00-3:25 The Effect of Rotation on Shoaling Internal Solitary WavesRoger Grimshaw, Loughborough


Tuesday, August 12

MS32Inverse Scattering Transform and Riemann--Hilbert Problems - Part II of III2:00 PM-4:00 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 1 see MS25 For Part 3 see MS40 Since the inverse scattering transform was introduced to linearize integrable nonlinear PDEs, a large body of knowledge has been accumulated on these systems. Riemann-Hilbert problems (RHPs) have proven to be a powerful tool for the study of integrable systems [e.g., in the formulation of the inverse problem and for asymptotic analysis of the solutions], and found many connections to other areas of pure and applied mathematics. The session aims at bringing together leading researchers in these areas, and at offering a broad overview of some of the current research activities at the frontier of pure and applied mathematics.



2:00-2:25 The Semiclassical Sine-Gordon and Rational Solutions of PainlevéIIPeter D. Miller, University of Michigan,

Ann Arbor, USA

2:30-2:55 A Spectral Approach to Dbar ProblemsChristian Klein, Institut de Mathématiques

de Bourgogne, France

3:00-3:25 Numerical Inverse Scattering for the Benjamin–Ono EquationSheehan Olver, University of Sydney,

Australia

3:30-3:55 Oscillatory Integrals and Integrable SystemsThomas Trogdon, Courant Institute


Tuesday, August 12

IP4Coherent Structures in 2D Turbulence: Identification and their Use1:00 PM-1:45 PMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Margaret Beck, Boston University, USA

Ideas from dynamical systems have recently provided fresh insight into transitional fluid flows. Viewing such flows as a trajectory through a phase space littered with coherent structures (meaning ‘exact’ solutions here) and their stable and unstable manifolds has proved a fruitful way of understanding such flows. Motivated by the challenge of extending this success to turbulent flows, I will discuss how coherent structures can be extracted directly from long-time simulations of body-forced turbulence on a 2D torus. These will then be used to ‘postdict’ certain statistics of the turbulence.

Rich KerswellUniversity of Bristol, United Kingdom



Tuesday, August 12

MS35Modeling of Optical Combs and Low-Noise Opto-Electronic Sources - Part III of III2:00 PM-4:00 PMRoom:Recital Room - Music Center

For Part 2 see MS28 In the past decade, new optical devices have been invented and old ones have been refined, leading to a dramatic decrease in the noise floor of time and frequency transfer devices. The devices include opto-electronic oscillators, comb lasers, microresonators, and narrow-linewidth continuous wave lasers. The range of applications is vast and includes astrophysics, telecommunications, medicine, and radio-frequency photonics. The modeling of these devices has not kept pace wit these experimental advances, which have opened up new theoretical problems that are related to solitons and nonlinear dynamics. In this minisymposium, we will highlight recent advances in modeling these devices and point to the new mathematical problems that they have opened.




2:00-2:25 Stability of Modelocked Lasers With Slow Saturable AbsorbersShaokang Wang and Curtis R. Menyuk,

University of Maryland, Baltimore County, USA

2:30-2:55 Terabit Communications Using Optical Frequency CombsChristian Koos, Karlsruhe Institute of

Technology, Germany

3:00-3:25 Noise of Frequency Combs Based on Yb Fiber Lasers with Self-Similar Pulse EvolutionWilliam Renninger, Yale University, USA

3:30-3:55 Novel Phenomena in WGM Resonators with Vertical Evanescent Coupling to Bus WaveguidesMher Ghulinyan, Fondazione Kessler, Italy

2:30-2:55 Ground States of a Nonlinear Curl-Curl ProblemThomas Bartsch, University of Giessen,

Germany; Tomas Dohnal, Technische Universität Dortmund, Germany; Michael Plum, Karlsruhe University, Germany; Wolfgang Reichel, Karlsruhe Institute of Technology, Germany

3:00-3:25 Analysis of Dispersion Managed Solitary WavesDirk Hundertmark, Karlsruhe Institute of

Technology, Germany

3:30-3:55 Reflection of an Incoming NLS Soliton by an Attractive Delta PotentialJustin Holmer and Quanhui Lin, Brown

University, USA

Tuesday, August 12

MS34Solitary Waves in Inhomogeneous Structures - Part II of III2:00 PM-4:00 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 1 see MS27 For Part 3 see MS42 The goal of the minisymposium is to discuss different aspects of Solitary waves (SW) in inhomogeneous structures, from analytical, numerical as well as applied points of view. On the one hand, there are results on the existence of SW in periodic media, e.g. asymptotics via envelope approximations and ground state solutions, and on wave propagation in media with variable (not necessarily periodic) coefficients. More recently, scattering of SW from strongly localized perturbations, e.g., delta potentials on the line or vertices in graphs has been studied. Important applications include dispersion management, waves at interfaces, in photonic crystals, waveguide arrays, and in networks.



2:00-2:25 On the Existence of Breathers in Periodic Media: An Approach Via Inverse Spectral TheoryMartina Chirilus-Bruckner, University

of Sydney, Australia; C. E. Wayne, Boston University, USA



Tuesday, August 12

MS38Nonlocal Wave Equations - Part I of II2:00 PM-4:00 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 2 see MS46 This session focuses on nonlocal model equations for wave problems in fluids and solids. Particular attention will be paid to equations in which the nonlocal character plays a crucial role in the behaviour of the solutions and in the analysis of the equations. Examples are the Benjamin-Ono equation which features algebraically decaying solutions, the Whitham equation which features a nonlocal operator of negative order, and the intermediate long wave equation. The topics under discussion include existence and stability of traveling waves and solitary waves, well posedness of the Cauchy problem, and singularity formation, as well as boundary value problems on finite and semi-infinite domains.

Organizer: Henrik KalischUniversity of Bergen, Norway

Organizer: Mats EhrnstromNorwegian University of Science and Technology, Norway

2:00-2:25 Dispersive Perturbations of Burgers and Hyperbolic EquationsFelipe Linares, Instituto de Matemática

Pura e Aplicada, Brazil; Didier Pilod, UFRJ, Brazil; Jean-Claude Saut, Universite de Paris-Sud, France

2:30-2:55 Three-Dimensional Solitary Water Waves with Weak Surface TensionBoris Buffoni, EPFL, France; Mark D.

Groves, Universität des Saarlandes, Germany; Erik Wahlen, Lund University, Sweden

3:00-3:25 Stability of Periodic Traveling Waves for Nonlocal Dispersive PDEMat Johnson, University of Kansas,

USA; Vera Hur, University of Illinois at Urbana-Champaign, USA

3:30-3:55 Local Well-posedness for a Class of Nonlocal Evolution Equations of Whitham TypeLong Pei, NTNU, Norway

Tuesday, August 12

MS37Solitons, Vortices, Domain Walls, Their Dynamics and Their Progenitors - Part I of III2:00 PM-4:00 PMRoom:Bevin Room - Wolfson Hall

For Part 2 see MS45 Understanding building blocks of solutions of key nonlinear partial differential equations, appearing in physics, material sciences, biology and other sciences, is of great current interest. These building blocks are highly symmetric (technically, equivariant), special solutions with high energy concentration and spatial localization. Examples of such solutions, which we will call ‘lumps’, are solitons, vortices, monopoles, domain walls (known also as interfaces or fronts), etc. Typically, a general solution can be represented as a collection of moving lumps interacting with each other and emitting radiation or dissipating. The dynamics of lumps and their relation to the underlying ‘microscopic’ dynamics will be the focus of the minisymposium.

Organizer: Israel Michael SigalUniversity of Toronto, Canada

Organizer: Avy SofferRutgers University, USA

2:00-2:25 Vortices and Vortex Lattices in the Ginzburg-Landau and Bcs TheoriesIsrael Michael Sigal, University of

Toronto, Canada

2:30-2:55 Two Component Condensates: Spin Orbit Coupling and DefectsAmandine Aftalion, CNRS and University

of Versailles, France

3:00-3:25 Convergence to an Equilibrium for Wave Maps on a Curved ManifoldPiotr Bizon, Jagiellonian University, Poland

3:30-3:55 A Gradient Flow Approach to the Keller-Segel SystemsAdrien Blanchet, TSE/IAST, GREMAQ,

Université de Toulouse, France

Tuesday, August 12

MS36Spectral and Geometric Methods in Stability of Waves and Patterns - Part IV of V2:00 PM-4:00 PMRoom:Club Room - Concourse (1st Floor)




2:00-2:25 Approximation of Traveling Waves on Finite IntervalsJens Rottmann-Matthes, Karlsruhe

Institute of Technology, Germany

2:30-2:55 Concatenated Traveling WavesStephen Schecter and Xiao-Biao Lin,

North Carolina State University, USA

3:00-3:25 Stability of Traveling Standing Waves for the Klein-Gordon EquationMilena Stanislavova, University of

Kansas, Lawrence, USA

3:30-3:55 Stability of Solitary Waves in Nonlinear Dirac EquationAndrew Comech, Texas A&M University,

USA and IITP, Moscow, Russia


Tuesday, August 12

MS40Inverse Scattering Transform and Riemann--Hilbert Problems - Part III of III4:30 PM-6:30 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS32 Since the inverse scattering transform was introduced to linearize integrable nonlinear PDEs, a large body of knowledge has been accumulated on these systems. Riemann-Hilbert problems (RHPs) have proven to be a powerful tool for the study of integrable systems [e.g., in the formulation of the inverse problem and for asymptotic analysis of the solutions], and found many connections to other areas of pure and applied mathematics. The session aims at bringing together leading researchers in these areas, and at offering a broad overview of some of the current research activities at the frontier of pure and applied mathematics.



4:30-4:55 On the Scattering Matrix for AKNS Systems with Matrix-Valued PotentialsMartin Klaus, Virginia Tech, USA

5:00-5:25 Large-degree Asymptotics of Generalised Hermite Polynomials and Poles of Rational Painlevé-IV FunctionsRobert Buckingham, University of

Cincinnati, USA

Tuesday, August 12

CP6Fluid Dynamics and Related Problems I2:00 PM-4:00 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Mark A. Hoefer, North Carolina State University, USA

2:00-2:15 Large Amplitude Solitary Waves and Dispersive Shock Waves in Conduits of Viscous Liquids: Experimental InvestigationMark A. Hoefer and Nicholas K. Lowman,


2:20-2:35 Large Amplitude Solitary Waves and Dispersive Shock Waves in Conduits of Viscous Liquids: Model Derivation and Modulation TheoryNicholas K. Lowman and Mark A. Hoefer,


2:40-2:55 Coherent Structures Inhibition and Destruction in the Taylor-Couette SystemOualli Hamid and Mekadem Mahmoud,

EMP, Algiers; Bouabdallah Ahcene, USTHB University, Algeria

3:00-3:15 Interaction of a Weak Discontinuity Wave with Elementary Waves of the Riemann Problem for Euler Equations of GasdynamicsVishnu D. Sharma, Indian Institute of

Technology-Bombay, India

3:20-3:35 On the Unified Wave Model (uwm) for Smooth and Peaked/cusped Solitary WavesShijun Liao, Shanghai Jiao Tong University,

China

3:40-3:55 Controlling the Position of Traveling Waves in Reaction-Diffusion SystemsJakob Löber and Harald Engel, Technical

University Berlin, Germany


Tuesday, August 12

MS39Dynamics of Spiral and Scroll Waves in Cardiac Tissue2:00 PM-4:00 PMRoom:JCR Games Room – Concourse (Ground Floor)

Spiral and scroll waves are nonlinear dissipative patterns occurring in 2- and 3-dimensional excitable media, respectively, where they act as (desired or undesired) organizing centers. Important example is excitation re-entry in the cardiac tissue where they underlie dangerous arrhythmias and fibrillation. Study of spiral and scroll dynamics by experimental, numerical and analytical approaches goes back nearly forty years. Recent advances in experimental, theoretical and computer simulation techniques brought the studies closer to practical applications than ever before. This minisymposium provides a sampling of the current state of experimental and theoretical research in this field.

Organizer: Irina BiktashevaUniversity of Liverpool, United Kingdom

2:00-2:25 Anatomy Induced Drift of Spiral Waves in Human AtriumIrina Biktasheva, University of

Liverpool, United Kingdom; Sanjay R. Kharche, University of Exeter, United Kingdom; Gunnar Seemann, Karlsruhe Institute of Technology, Germany; Henggui Zhang, The University of Manchester, UK; Vadim N. Biktashev, University of Exeter, United Kingdom

2:30-2:55 Optogenetic Control of Cardiac Electrical Activity: Experimental InsightsEmilia Entcheva, Stony Brook

University, USA

3:00-3:25 Spatiotemporal Dynamics of Obstacle-Induced Spiral Wave InitiationThomas D. Quail, McGill University,

Canada

3:30-3:55 Exact Coherent Structures and Dynamics of Cardiac TissueGreg A. Byrne, Chris Marcotte, and

Roman Grigoriev, Georgia Institute of Technology, USA



Tuesday, August 12

MS42Solitary Waves in Inhomogeneous Structures - Part III of III4:30 PM-6:30 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS34 The goal of the minisymposium is to discuss different aspects of Solitary waves (SW) in inhomogeneous structures, from analytical, numerical as well as applied points of view. On the one hand, there are results on the existence of SW in periodic media, e.g. asymptotics via envelope approximations and ground state solutions, and on wave propagation in media with variable (not necessarily periodic) coefficients. More recently, scattering of SW from strongly localized perturbations, e.g., delta potentials on the line or vertices in graphs has been studied. Important applications include dispersion management, waves at interfaces, in photonic crystals, waveguide arrays, and in networks.



4:30-4:55 The NLS on Fat Graphs and the Metric Graph LimitHannes Uecker, University of Oldenburg,

Germany; Zarif A. Sobirov, Tashkent State University, Uzbekistan

5:00-5:25 Minimizing the NLS Energy on General GraphsRiccardo Adami, Enrico Serra, and Paolo

Tilli, Politecnico di Torino, Italy

5:30-5:55 Micro/macroscopic Models for Fluid Flow in Networks of Elastic TubesRadu C. Cascaval, University of

Colorado, Colorado Springs, USA

6:00-6:25 Solution Formulas for the Linearized KdV Equation on GraphsZarif A. Sobirov, Tashkent State

University, Uzbekistan; Hannes Uecker, University of Oldenburg, Germany; Maksad Akhmedov, Tashkent State University, Uzbekistan

Tuesday, August 12

MS41Nonlinear Waves in Geophysical Fluid Dynamics - Part III of III4:30 PM-6:30 PMRoom:Jock Colville Hall - Archives Center

For Part 2 see MS33 Nonlinear waves in the atmosphere and in the ocean bring together researchers from many different, but related, fields with a wide range of applications together with interesting mathematical developments.



4:30-4:55 Tropical-Extratropical Wave Interactions in a Moist 2-Layer ModelJuliana F. Dias, NOAA Earth System

Research Laboratory

5:00-5:25 The Influence of Fast Waves and Fluctuations on the Evolution Three Slow Limits of the Boussinesq EquationsBeth Wingate, University of Exeter, United

Kingdom; Jared Whitehead, Brigham Young University, USA; Terry Haut, Los Alamos National Laboratory, USA

5:30-5:55 Nonlinear Wave Interactions in Global Nonhydrostatic ModelsCarlos Raupp and Andre Teruya,

University of Sao Paulo, Brazil

6:00-6:25 Pilot Wave Dynamics in a Rotating Frame: Orbital Quantization and Multimodal StatisticsAnand Oza, Massachusetts Institute of

Technology, USA

5:30-5:55 Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equation with Asymmetric Nonzero Boundary ConditionsGino Biondini and Emily Fagerstrom,

State University of New York, Buffalo, USA; Barbara Prinari, University of Colorado, Colorado Springs, USA

6:00-6:25 Inverse Scattering Transform for the Focusing NLS Equation with Fully Asymmetric Boundary ConditionsFrancesco Demontis, Universita di Cagliari,

Italy; Barbara Prinari, University of Colorado, Colorado Springs, USA; Cornelis Van der Mee, Universita di Cagliari, Italy; Federica Vitale, Università del Salento, Italy


Tuesday, August 12

MS45Solitons, Vortices, Domain Walls, Their Dynamics and Their Progenitors - Part II of III4:30 PM-5:30 PMRoom:Bevin Room - Wolfson Hall

For Part 1 see MS37 For Part 3 see MS53 Understanding building blocks of solutions of key nonlinear partial differential equations, appearing in physics, material sciences, biology and other sciences, is of great current interest. These building blocks are highly symmetric (technically, equivariant), special solutions with high energy concentration and spatial localization. Examples of such solutions, which we will call ‘lumps’, are solitons, vortices, monopoles, domain walls (known also as interfaces or fronts), etc. Typically, a general solution can be represented as a collection of moving lumps interacting with each other and emitting radiation or dissipating. The dynamics of lumps and their relation to the underlying ‘microscopic’ dynamics will be the focus of the minisymposium.



4:30-4:55 Regularity and Stability of Landau-Lifshitz FlowsStephen Gustafson, University of British

Columbia, Canada

5:00-5:25 Dynamics of Bec of Fermion Pairs in the Low Density Limit of Bcs TheoryChristian Hainzl, University of Tuebingen,

Germany

Tuesday, August 12

MS44Spectral and Geometric Methods in Stability of Waves and Patterns - Part V of V4:30 PM-6:30 PMRoom:Club Room - Concourse (1st Floor)

For Part 4 see MS36 The purpose of this session is to bring together researchers working on various stability issues for such special solutions of partial differential equations as patterns and waves. All aspects of stability/instability will be discussed, from spectral to nonlinear, with special emphasis on methods of spectral theory. It is expected that the speakers will spend some time of their talks to address possible perspectives in the field of their work as we believe that such a perspective would be not only interesting for the audience but it can also stimulate further discussion and further research in the field.



4:30-4:55 Evans Function Analysis of Viscous Multidimensional Shock LayersJeffrey Humpherys, Brigham Young

University, USA; Greg Lyng, University of Wyoming, USA; Kevin Zumbrun, Indiana University, USA

5:00-5:25 Computing the Refined Stability Condition for Shock WavesGregory Lyng, University of Wyoming,

USA

5:30-5:55 The Evolution of Traveling Waves in a Simple Isothermal Chemical SystemJe-Chiang Tsai, National Chung Cheng

University, Taiwan

6:00-6:25 Linear and Spectral Stability of Solitary Gravity WavesShu-Ming Sun, Virginia Tech, USA

Tuesday, August 12

MS43Nonlinear Waves in Systems with PT Symmetry - Part I of III4:30 PM-7:00 PMRoom:Recital Room - Music Center

For Part 2 see MS51 Interest in the so-call parity-time (PT)–symmetric systems, i.e., systems described by non-Hermitian Hamiltonians with real spectra, is rapidly growing during the last fifteen years. Recently, studies of nonlinear PT-symmetric systems became particularly intensive, since the respective models were shown to be of great relevance for many branches of physics such as optics, Bose-Einstein condensates, electronics, and so on. The purpose of this minisymposium is to highlight effects due to the interplay between nonlinearity and PT-symmetry and overview their physical applications.

Organizer: Vladimir V. KonotopUniversity of Lisbon, Portugal

Organizer: Jianke YangUniversity of Vermont, USA

4:30-4:55 Coupled PT-Symmetric SystemsCarl M. Bender, Washington University

in St. Louis, USA

5:00-5:25 New Aspects of Nonlinear PT-Symmetric PlaquettesUwe Guenther, Helmholtz-Center

Dresden-Rossendorf, Germany

5:30-5:55 One AC and Two PT Nonlinear Schrödinger DimersIgor Barashenkov, University of Cape

Town, South Africa

6:00-6:25 Linear and Nonlinear Properties of PT-symmetric Optical SystemsDemetrios Christodoulides, University

of Central Florida, USA

6:30-6:55 Pt-Symmetric Synthetic MaterialsKonstantinos Makris, Princeton

University, USA; Stefan Rotter, Vienna University of Technology, Austria; Demetrios Christodoulides, University of Central Florida, USA


Tuesday, August 12

CP7Patterns and Related Problems4:30 PM-6:30 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Alastair M. Rucklidge, University of Leeds, United Kingdom

4:30-4:45 Hopf Bifurcation from Fronts in the Cahn-Hilliard EquationRyan Goh and Arnd Scheel, University of

Minnesota, USA

4:50-5:05 New Exact Solution for Nonlinear Interaction of Two Pulsatory Waves of the Korteweg – De Vries Equation in An Invariant Zigzag StructureVictor A. Miroshnikov, College of

Mount Saint Vincent, USA

5:10-5:25 Inertial Waves and Pattern Formation Inside a Rotating Cylinder Partially Filled with LiquidDenis A. Polezhaev, Victor Kozlov,

and Veronika Dyakova, Perm State Humanitarian Pedagogical University, Perm, Russia

5:30-5:45 Quasipatterns in Coupled Reaction-Diffusion ProblemsAlastair M. Rucklidge, University of

Leeds, United Kingdom

5:50-6:05 Vibrational Hydrodynamic Top Wave Instability and Pattern FormationStanislav Subbotin, Victor Kozlov,

and Nikolay Kozlov, Perm State Humanitarian Pedagogical University, Perm, Russia

6:10-6:25 Oscillons in a Parametrically Forced PDEAlastair M. Rucklidge, Abeer Al-Nahdi,

and Jitse Niesen, University of Leeds, United Kingdom

Dinner Break6:30 PM-8:00 PMAttendees on their own.

Meals will be available for purchase in the Dining Room or Buttery snack bar.

Tuesday, August 12

MS47Theoretical Aspects of Spiral and Scroll Waves Dynamics4:30 PM-7:00 PMRoom:JCR Games Room – Concourse (Ground Floor)

Spiral and scroll waves are nonlinear dissipative patterns occurring in 2- and 3-dimensional excitable media, respectively, where they act as (desired or undesired) organizing centers. Recent experimental studies of biological and chemical excitable systems help to form novel views on spiral and scroll waves dynamics, interaction of scroll wave filaments and spiral tips with each other, with gradients, boundaries and local inhomogeneities. The minisymposium provides a sampling of the current state of theoretical and experimental research in the field and related numerical modeling.

Organizer: Roman GrigorievGeorgia Institute of Technology, USA

4:30-4:55 Dynamics of Spiral Cores: the Effect of Boundaries and HeterogeneitiesRoman Grigoriev, Christopher Marcotte,

and Greg Byrne, Georgia Institute of Technology, USA

5:00-5:25 Spiral PinballsJacob Langham and Dwight Barkley,

University of Warwick, United Kingdom

5:30-5:55 Measuring Scroll Filament RigidityVadim N. Biktashev, University of Exeter,

United Kingdom; Elias Nakouzi, Zulma Jimenez, and Oliver Steinbock, Florida State University, USA

6:00-6:25 Effective Dynamics of Twisted and Curved Scroll Waves Using Virtual FilamentsHans Dierckx, Ghent University, Belgium

6:30-6:55 Kinematic Theory of Spirals and Wave SegmentsVladimir Zykov and Eberhard Bodenschatz,

Max-Planck-Institute for Dynamics and Self-Organization, Germany

Tuesday, August 12

MS46Nonlocal Wave Equations - Part II of II4:30 PM-6:30 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 1 see MS38 This session focuses on nonlocal model equations for wave problems in fluids and solids. Particular attention will be paid to equations in which the nonlocal character plays a crucial role in the behaviour of the solutions and in the analysis of the equations. Examples are the Benjamin-Ono equation which features algebraically decaying solutions, the Whitham equation which features a nonlocal operator of negative order, and the intermediate long wave equation. The topics under discussion include existence and stability of traveling waves and solitary waves, well posedness of the Cauchy problem, and singularity formation, as well as boundary value problems on finite and semi-infinite domains.

Organizer: Henrik KalischUniversity of Bergen, Norway

Organizer: Mats EhrnstromNorwegian University of Science and Technology, Norway

4:30-4:55 Pseudodifferential Operators on a Half-line and the Riemann-Hilbert ProblemElena Kaikina, National Autonomous

University of Mexico, Mexico

5:00-5:25 Stability of Solitary Waves for the Doubly Dispersive Nonlinear Wave EquationHusnu Ata Erbay and Saadet Erbay,

Ozyegin University, Turkey; Albert Erkip, Sabanci University, Turkey

5:30-5:55 Dissipation and Dispersion in Shallow WaterJohn Carter, Seattle University, USA;

Harvey Segur, University of Colorado, USA; David L. George, U.S. Geological Survey, USA

6:00-6:25 A Numerical Method for Computing Traveling Waves of Nonlinear Dispersive EquationsDaulet Moldabayev, University of Bergen,

Norway


On the Statistics of Localized Rogue Wave Structures in Spontaneous Modulation InstabilityJohn Dudley, Université de Franche-Comté,

France; Shanti Toenger, FEMTO-ST Institute, France; Goery Genty, Tampere University of Technology, Finland; Frederic Dias, University College Dublin, Ireland

Evolution Equations for Weakly Nonlinear Internal Ocean WavesEric J. Tovar, Daqi Xin, and Zhijun Qiao,

University of Texas - Pan American, USA

Reflection and Transmission of Plane Quasi Longitudinal Waves at Semiconductor Elastic Solid InterfaceAmit Sharma, National Institute of

Technology Hamirpur, India

Soliton Interactions in the Sasa-Satsuma Equation on Nonzero BackgroundsTao Xu, China University of Petroleum,

China; Min Li, North China Electric Power University, China

Abundant Soliton Solutions of the General Nonlocal Nonlinear Schrodinger System with the External FieldJi Lin, Zhejiang Normal University, China;

Xiaoyan Tang, East China Normal University, China

Elastic Nonlineal Model for a Unidimensional Chain with Clustering ZonesFrancisco J. Martinez, Universidad

Nacional Autónoma de México, Mexico

Scattering from a Large Cylinder with a Cluster of Eccentrically Embedded CoresBrittany Mccollom, Colorado School

of Mines, USA; Alex Yuffa, U.S. Army Research Laboratory, USA

Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion EquationsKelly Mcquighan and Bjorn Sandstede,

Brown University, USA

Stability of Morphodynamical Equilibria in Tidal BasinsCorine J. Meerman and Vivi Rottschäfer,

Leiden University, Netherlands; Henk Schuttelaars, Delft University of Technology, Netherlands

Hydrodynamic Rogue WavesDaniel Ratliff, University of Surrey, United

Kingdom

Bifurcation of Travelling Waves in Nonlinear Magnetic Meta-MaterialsVassilis M. Rothos, Aristotle University

of Thessaloniki, Greece; Hadi Sussanto, University of Essex, United Kingdom; G.P Veldes, Technological Institution of Lamia, Greece

Tracking Pattern Evolution Beyond Center Manifold Reductions with Singular PerturbationsLotte Sewalt, Arjen Doelman, and

Vivi Rottschäfer, Leiden University, Netherlands; Antonios Zagaris, University of Twente, Netherlands

Robust Pulse Generators in An Excitable Medium with Jump-Type HeterogeneityTakashi Teramoto, Asahikawa Medical

University, Japan

Tuesday, August 12

PP1Reception and Poster Session8:00 PM-10:00 PMRoom:Buttery - Concourse (Ground Floor)

Bifurcation of Travelling Waves in Nonlinear Magnetic MetamaterialsMakrina Agaoglou, Makrina Agaoglou,

and Vassilis M. Rothos, Aristotle University of Thessaloniki, Greece; Hadi Susanto, University of Essex, United Kingdom; Giorgos P. Veldes, University of Athens, Greece

The Dual-Weighted Residual Method Applied to a Discontinuous Galerkin Discretization for the Shallow Water Wave EquationsSusanne Beckers, University of

Hamburg, Germany; Jörn Behrens, KlimaCampus - University of Hamburg, Germany; Winnifried Wollner, University of Hamburg, Germany

Dipolar Bose-Einstein CondensatesRoberto I. Ben, Universidad Nacional de

General Sarmiento, Argentina

Oscillatory Pulses in the Fitzhugh-Nagumo EquationPaul A. Carter and Bjorn Sandstede,


Stability of Spatially Periodic Pulse Solutions in General Singularly Perturbed Reaction-Diffusion SystemsBjörn De Rijk and Arjen Doelman,

Leiden University, Netherlands; Jens Rademacher, University of Bremen, Germany; Frits Veerman, Oxford University, United Kingdom

Stochastic Mode-Reduction in Models with Conservative Fast Sub-SystemsAnkita Jain, University of Notre Dame,

USA

Stochastic Analysis of Turbulent MixingHyeonseong Jin, Jeju National

University, South Korea

continued in next columncontinued in next column



MS49Existence, Stability and Evolution of Coherent Structures in Coupled Systems - Part I of II8:10 AM-10:10 AMRoom:Jock Colville Hall - Archives Center

For Part 2 see MS57 This special session will bring together researchers who study fronts, pulses, wave trains and patterns of complex structures, which occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The speakers in this special session will present their results on the existence, stability, dynamical properties, and bifurcations of these solutions in coupled systems obtained using analytical and numerical techniques.

Organizer: Stephane LafortuneCollege of Charleston, USA

Organizer: Vahagn ManukianMiami University, USA

8:10-8:35 Spatially Periodic Patterns, Busse Balloons, and the Hopf DanceArjen Doelman and Björn De Rijk,

Leiden University, Netherlands; Jens Rademacher, University of Bremen, Germany; Frits Veerman, Oxford University, United Kingdom

8:40-9:05 Pattern Formation in a Class of Landau-Lifschitz-Gilbert-Slonczewski Equations for Spintronic DevicesJens Rademacher, University of Bremen,

Germany

9:10-9:35 Modulation Equations for Interacting Localized StructuresMartina Chirilus-Bruckner, University

of Sydney, Australia

9:40-10:05 Coherent Structures in a Population Model for Mussel-Algae InteractionAnna Ghazaryan, Miami University and

University of Kansas, USA; Vahagn Manukian, Miami University, USA

8:10-8:35 Nondecaying Solutions of KdV EquationVladimir E. Zakharov, University

of Arizona, Tucson and Lebedev Physical Institute, Moscow, Russia; Dmitry Zakharov, Courant Institute of Mathematical Sciences, New York University, USA

8:40-9:05 Surface Waves in Graded Index Meta-materialsIldar R. Gabitov, University of Arizona

and Los Alamos National Laboratory, USA; Andrei Maimistov, Moscow Engineering Physics Institute, Russia

9:10-9:35 Channel Capacity and Nonlinear Fourier Transform in Coherent Fibre-Optic CommunicationsSergei Turitsyn, Aston University, United

Kingdom

9:40-10:05 Models for Laser-Driven Generation of THz RadiationPedro Gonzalez de Alaiza and Luc Berge,

CEA, France



MS48Nonlinear Waves, Singularities, and Collapses in Water Waves, Optics and Plasmas - Part I of IV8:10 AM-10:10 AMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS56 Waves dynamics is one of the most interesting and appealing problems in applied mathematics and physics. In wast majority of interesting cases the problem of wave propagation can be solved not only in the linear approximation but also with nonlinear effects taken into account, due to powerful tools of modern applied mathematics and theoretical physics. Common approaches stimulate intensive interchange of ideas in the field which accelerates the development of the wave dynamics even further. Our minisymposium is devoted to new advances in the theory of waves and demonstrates vividly the similarity of approaches in a broad spectrum of important applications.

Organizer: Alexander O. KorotkevichUniversity of New Mexico, USA

Organizer: Pavel M. LushnikovUniversity of New Mexico, USA




MS52Algebraic Aspects of Integrable Systems and Applications - Part I of IV8:10 AM-10:10 AMRoom:Club Room - Concourse (1st Floor)

For Part 2 see MS60 Integrable system has been studied extensively in related to many fields in both pure mathematics and applied mathematics. Meanwhile, the integrable system also promises applications ranging from water waves, nonlinear optics to numerical algorithms. The purpose of this special session is to bring together researchers from integrable system in both continuous and discrete integrable system to discuss recent advances on algebraic aspects of integrable systems and their applications.

Organizer: Bao-Feng FengUniversity of Texas - Pan American, USA

Organizer: Xing-Biao HuChinese Academy of Sciences, China

Organizer: Kenichi MarunoUniversity of Texas - Pan American, USA

Organizer: Jonathan NimmoUniversity of Glasgow, Scotland, United Kingdom

8:10-8:35 On Jost Solutions for the Discrete and Ultradiscrete KdV EquationJonathan Nimmo, University of Glasgow,

Scotland, United Kingdom

8:40-9:05 Classification of Tau-symmetric Hamiltonian Evolutionary PDEsYoujin Zhang, Tsinghua University, P. R.

China

9:10-9:35 Quasi-Determinants and Non Commutative Equations with Pfaffian Type SolutionsClaire Gilson, University of Glasgow,

Scotland, United Kingdom

9:40-10:05 A Four-component Camassa-Holm Type HierarchyQingping Liu, China University of Mining

and Technology, China


MS51Nonlinear Waves in Systems with PT Symmetry - Part II of III8:10 AM-10:10 AMRoom:Recital Room - Music Center

For Part 1 see MS43 For Part 3 see MS59 Interest in the so-call parity-time (PT)–symmetric systems, i.e., systems described by non-Hermitian Hamiltonians with real spectra, is rapidly growing during the last fifteen years. Recently, studies of nonlinear PT-symmetric systems became particularly intensive, since the respective models were shown to be of great relevance for many branches of physics such as optics, Bose-Einstein condensates, electronics, and so on. The purpose of this minisymposium is to highlight effects due to the interplay between nonlinearity and PT-symmetry and overview their physical applications.



8:10-8:35 CPT-symmetric Spin-orbit-coupled CondensateYaroslav Kartashov, Institut de Ciències

Fotòniques, Spain; Vladimir V. Konotop, University of Lisbon, Portugal; Dmitry Zezyulin, Universidade de Lisboa, Portugal

8:40-9:05 Nonlinear Dynamics in PT-Symmetric LatticesDmitry Pelinovsky, McMaster University,

Canada

9:10-9:35 Asymmetric Transport in Non-Linear Systems with Parity-Time SymmetryTsampikos Kottos, Wesleyan University,

USA

9:40-10:05 Interactions of Bright and Dark Solitons with Localized PT-Symmetric PotentialsBoris Malomed, Tel Aviv University, Israel;

Hadi Susanto, University of Essex, United Kingdom


MS50Water Waves with Surface Tension - Part I of II8:10 AM-10:10 AMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS58 Water waves have been studied for over 200 years, but many fundamental questions remain about their behaviour. One of these questions is about the role of surface tension in various models. In this session, we will explore this and similar questions analytically and numerically.

Organizer: Olga TrichtchenkoUniversity of Washington, USA


8:10-8:35 Lasers and RipplesPaul A. Milewski, University of

Bath, United Kingdom; Zhan Wang, University College London, United Kingdom

8:40-9:05 Stability of Near-Resonant Gravity-Capillary WavesOlga Trichtchenko and Bernard

Deconinck, University of Washington, USA

9:10-9:35 The Influence of Surface Tension Upon Trapped Waves and Hydraulic FallsEmilian I. Parau and Charlotte Page,

University of East Anglia, United Kingdom

9:40-10:05 Dimension-Breaking Phenomena for Solitary Gravity-Capillary Water WavesMark D. Groves, Universität des

Saarlandes, Germany; Shu-Ming Sun, Virginia Tech, USA; Erik Wahlen, Lund University, Sweden



MS55Nonlinear Waves in Metamaterials: Theory and Applications - Part I of II8:10 AM-9:40 AMRoom:JCR Games Room – Concourse (Ground Floor)

For Part 2 see MS63 Recently, artificially constructed metamaterials have attracted considerable interests because of their nontrivial and peculiar electromagnetic properties. Understanding nonlinear wave propagations in the systems are of importance, not only from the application, but also from the mathematical point of view. The minisymposium aims to bring together experts from the field of metamaterials and related areas, including but not limited to the creations and characteristics of localised structures in the systems. The target of the minisymposium is to present recent contributions to this subject, both theoretically and experimentally.

Organizer: Vassilis M. RothosAristotle University of Thessaloniki, Greece

Organizer: Hadi SusantoUniversity of Essex, United Kingdom

8:10-8:35 Nonlinear Waves in a Homogenized Two-Phase Particulate Composite MediumNikolaos L. Tsitsas, Aristotle University

of Thessaloniki, Greece; Akhlesh Lakhtakia, Pennsylvania State University, USA; Dimitri Frantzeskakis, University of Athens, Greece

8:40-9:05 Nonlinear Wave Propagation and Localization in Squid MetamaterialsNikos Lazarides and George Tsironis,

University of Crete, Greece

9:10-9:35 Dynamical Properties of Parity-Time Symmetric MetamaterialsGeorge Tsironis, University of Crete,

Greece


MS54Connections Between Nonlinear Wave Equations and Geometry - Part I of III8:10 AM-10:10 AMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 2 see MS62 This minisymposium will discuss some of the many facets of the interplay between geometry and nonlinear wave equations, and its increasingly important role in the study of nonlinear PDE and integrable systems, as well as differential and Poisson geometry. Topics will include geometric evolution equations---both continuous and discrete---arising in physical or geometric settings, geometric aspects of nonlinear wave equations (such as recursion operators and Poisson structures), and existence and construction of special solutions and coherent structures through geometric methods (e.g. Inverse Scattering Transform, Bäcklund transformations, algebro-geometric tools, Hirota method, etc.).

Organizer: Annalisa M. CaliniCollege of Charleston, USA

Organizer: Francesco DemontisUniversita di Cagliari, Italy

Organizer: Giovanni OrtenziUniversity of Milan, Italy

8:10-8:35 Discrete Geometry of Polygons and Hamiltonian StructuresGloria Mari Beffa, University of Wisconsin,

Madison, USA

8:40-9:05 Discrete Moving Frames and Discrete Integrable SystemsJin-Ping Wang, University of Kent, United

Kingdom

9:10-9:35 Discrete KP Equation with Self-Consistent SourcesAdam Doliwa, University of Warmia and

Mazury, Poland; Runliang Lin, Tsinghua University, P. R. China

9:40-10:05 Geometric Aspects of Integrable Self-adaptive Moving Mesh SchemesKenichi Maruno, University of Texas - Pan

American, USA


MS53Solitons, Vortices, Domain Walls, Their Dynamics and Their Progenitors - Part III of III8:10 AM-10:10 AMRoom:Bevin Room - Wolfson Hall

For Part 2 see MS45 Understanding building blocks of solutions of key nonlinear partial differential equations, appearing in physics, material sciences, biology and other sciences, is of great current interest. These building blocks are highly symmetric (technically, equivariant), special solutions with high energy concentration and spatial localization. Examples of such solutions, which we will call ‘lumps’, are solitons, vortices, monopoles, domain walls (known also as interfaces or fronts), etc. Typically, a general solution can be represented as a collection of moving lumps interacting with each other and emitting radiation or dissipating. The dynamics of lumps and their relation to the underlying ‘microscopic’ dynamics will be the focus of the minisymposium.



8:10-8:35 Vorticity Models in Condensed Matter Physics and Gradient Flows of 1-Homogeneous FunctionalsGiandomenico Orlandi, University of

Verona, Italy

8:40-9:05 Coherent Motion in Hamiltonian Lattices with Next-to-nearest Neighbour InteractionsJohannes Zimmer and Christine Venney,

University of Bath, United Kingdom

9:10-9:35 Skyrmions as Models of NucleiNicholas Manton, University of


9:40-10:05 Long Range Scattering for the Klein-Gordon Equation with Nonhomogeneous NonlinearitiesAvy Soffer, Rutgers University, USA



IP6Engineering Extreme Materials with Defects and Nonlinearity1:00 PM-1:45 PMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Apala Majumdar, University of Bath, United Kingdom

We study the fundamental dynamic response of discrete nonlinear systems and study the effects of defects in the energy localization and propagation. We exploit this understanding to create experimentally novel materials and devices at different scales (for example, for application in energy absorption, acoustic imaging and energy harvesting). We use granular systems as a basic platform for testing, and control the constitutive behavior of the new materials selecting the particles’ geometry, their arrangement and materials properties. Ordered arrangements of particles exhibit a highly nonlinear dynamic response, which has opened the door to exciting fundamental physical observations (i.e., compact solitary waves, energy trapping phenomena, and acoustic rectification). This talk will focus on energy localization and redirection in one- and two-dimensional systems.

Chiara DaraioETH Zürich, Switzerland and California Institute of Technology, USA



IP5A Neural Field Model of Binocular Rivalry Waves10:45 AM-11:30 AMRoom:Wolfson Auditorium - Wolfson Hall

Chair:Alina Chertock, North Carolina State University, USA

Binocular rivalry is the phenomenon where perception switches back and forth between different images presented to the two eyes. The resulting fluctuations in perceptual dominance and suppression provide a basis for non-invasive studies of the human visual system and the identification of possible neural mechanisms underlying conscious visual awareness. In this talk we present a neural field model of binocular rivalry waves in visual cortex – continuum neural fields are integro-differential equations that describe the large-scale spatiotemporal dynamics of neuronal populations. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. We then analyze the effects of extrinsic noise on wave propagation in a stochastic version of the neural field model. We end by describing recent work on rotating rivalry stimuli and direction selectivity.

Paul C. BressloffUniversity of Utah, USA and University of Oxford, United Kingdom




CP8Dynamical Systems and Related Problems8:10 AM-9:50 AMRoom:Tizard Room - Concourse (1st Floor)

Chair: Richard Kollar, Comenius University, Bratislava, Slovakia

8:10-8:25 Pullback Attractor for the Non-Autonomous Stochastic Damped Wave Equations on Bounded and Unbounded DomainsHongyan Li, Shanghai University of

Engineering Science, China

8:30-8:45 Persistence Results for Nonlocal Perturbations on Unbounded DomainsChristian Kuehn and Franz Achleitner,

Vienna University of Technology, Austria

8:50-9:05 New Criteria Preventing Hamiltonian-Hopf Bifurcations Using Graphical Krein SignatureRichard Kollar, Comenius University,

Bratislava, Slovakia; Peter Miller, University of Michigan, USA

9:10-9:25 Complex Mode Dynamics of Coupled Wave OscillatorsTristram J. Alexander, University of

New South Wales, Australia; Dong Yan and P. Kevrekidis, University of Massachusetts, USA

9:30-9:45 Modulation Theory for the Fkdvb Equation Constructing Periodic SolutionsLaura Hattam, Monash University,

Australia


Remarks10:40 AM-10:45 AMRoom:Wolfson Auditorium - Wolfson Hall



MS57Existence, Stability and Evolution of Coherent Structures in Coupled Systems - Part II of II2:00 PM-4:00 PMRoom:Jock Colville Hall - Archives Center

For Part 1 see MS49 This special session will bring together researchers who study fronts, pulses, wave trains and patterns of complex structures, which occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The speakers in this special session will present their results on the existence, stability, dynamical properties, and bifurcations of these solutions in coupled systems obtained using analytical and numerical techniques.

Organizer: Stephane LafortuneCollege of Charleston, USA

Organizer: Vahagn ManukianMiami University, USA

2:00-2:25 Vortex Dynamics in Bose-Einstein Condensates: Bifurcations, Chaotic Dynamics and Experimental ObservationsPanayotis Kevrekidis, University of

Massachusetts, Amherst, USA

2:30-2:55 Traveling Waves in Holling-Tanner Model with DiffusionVahagn Manukian and Anna

Ghazaryan, Miami University, USA

3:00-3:25 Semi-strong Multipulse Interaction in Reaction Diffusion Systems: The Case of Asymptotically Weak DissipationKeith Promislow, Michigan State

University, USA; Arjen Doelman, Leiden University, Netherlands; Tom Bellsky, Arizona State University, USA

3:30-3:55 Dynamics of Vortex Filaments and their StabilityAnnalisa M. Calini, College of

Charleston, USA

3:00-3:25 Instabilities of Gravity and Capillary Waves on the Surface of the FluidAlexander O. Korotkevich, University

of New Mexico, USA; Alexander Dyachenko, Landau Institute for Theoretical Physics, Russia; Vladimir E. Zakharov, University of Arizona, Tucson and Lebedev Physical Institute, Moscow, Russia

3:30-3:55 Some Fundamental Issues in Internal Wave DynamicsRoberto Camassa, University of North

Carolina, Chapel Hill, USA


MS56Nonlinear Waves, Singularities, and Collapses in Water Waves, Optics and Plasmas - Part II of IV2:00 PM-4:00 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 1 see MS48 For Part 3 see MS64 Waves dynamics is one of the most interesting and appealing problems in applied mathematics and physics. In wast majority of interesting cases the problem of wave propagation can be solved not only in the linear approximation but also with nonlinear effects taken into account, due to powerful tools of modern applied mathematics and theoretical physics. Common approaches stimulate intensive interchange of ideas in the field which accelerates the development of the wave dynamics even further. Our minisymposium is devoted to new advances in the theory of waves and demonstrates vividly the similarity of approaches in a broad spectrum of important applications.



2:00-2:25 Blowup Dynamics in the Keller-Segel Model of ChemotaxisIsrael Michael Sigal, University of

Toronto, Canada

2:30-2:55 Modeling Combined UV/IR FilamentationAlejandro Aceves, Southern Methodist

University, USA




MS60Algebraic Aspects of Integrable Systems and Applications - Part II of IV2:00 PM-4:00 PMRoom:Club Room - Concourse (1st Floor)

For Part 1 see MS52 For Part 3 see MS68 Integrable system has been studied extensively in related to many fields in both pure mathematics and applied mathematics. Meanwhile, the integrable system also promises applications ranging from water waves, nonlinear optics to numerical algorithms. The purpose of this special session is to bring together researchers from integrable system in both continuous and discrete integrable system to discuss recent advances on algebraic aspects of integrable systems and their applications.





2:00-2:25 On Exact Solutions to Lattice EquationsDaisuke Takahashi, Waseda University,

Japan

2:30-2:55 Constructing Probabilistic Particle Cellular Automata from Fundamental DiagramsJunta Matsukidaira, Ryukoku University,

Japan

3:00-3:25 Soliton Solutions to an Extended Box and Ball System EquationHidetomo Nagai, Tokai University, Japan

3:30-3:55 Lattice Boussinesq Equation and Convergence Acceleration AlgorithmsYi He, Chinese Academy of Sciences, China


MS59Nonlinear Waves in Systems with PT Symmetry - Part III of III2:00 PM-4:00 PMRoom:Recital Room - Music Center

For Part 2 see MS51 Interest in the so-call parity-time (PT)–symmetric systems, i.e., systems described by non-Hermitian Hamiltonians with real spectra, is rapidly growing during the last fifteen years. Recently, studies of nonlinear PT-symmetric systems became particularly intensive, since the respective models were shown to be of great relevance for many branches of physics such as optics, Bose-Einstein condensates, electronics, and so on. The purpose of this minisymposium is to highlight effects due to the interplay between nonlinearity and PT-symmetry and overview their physical applications.



2:00-2:25 Partially- PT -symmetric Potentials with All-real Spectra and Soliton FamiliesJianke Yang, University of Vermont, USA

2:30-2:55 Solitons in Quadratically Nonlinear Media with PT-Symmetric PotentialsFatkhulla Abdullaev and Bakhram Umarov,

International Islamic University of Malaysia, Malaysia

3:00-3:25 Dynamical Theory of Scattering for Complex Potentials, Inverse Scattering, and Confined NonlinearitiesAli Mostafazadeh, Koc University, Turkey

3:30-3:55 Nonlinear Quantum Dynamics of a BEC in a PT-symmetric Double-well TrapHolger Cartarius, Daniel Haag, Dennis

Dast, Andreas Löhle, Jörg Main, and Günter Wunner, Universität Stuttgart, Germany


MS58Water Waves with Surface Tension - Part II of II2:00 PM-4:00 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 1 see MS50 Water waves have been studied for over 200 years, but many fundamental questions remain about their behaviour. One of these questions is about the role of surface tension in various models. In this session, we will explore this and similar questions analytically and numerically.

Organizer: Olga TrichtchenkoUniversity of Washington, USA


2:00-2:25 Gravity Capillary Waves and Related ProblemsJean-Marc Vanden-Broeck, University

College London, United Kingdom

2:30-2:55 A Quasi-Planar Model for Gravity-Capillary Interfacial Waves in Deep WaterZhan Wang, University College London,

United Kingdom

3:00-3:25 An Efficient Boundary Integral Method for 3D Interfacial Flow with Surface Tension: Numerical Results and Numerical AnalysisDavid Ambrose, Drexel University, USA

3:30-3:55 A Reduction of the Euler Equations to a Single Time-Dependent EquationKatie Oliveras, Seattle University,

USA; Vishal Vasan, Pennsylvania State University, USA



MS63Nonlinear Waves in Metamaterials: Theory and Applications - Part II of II2:00 PM-3:30 PMRoom:JCR Games Room – Concourse (Ground Floor)

For Part 1 see MS55 Recently, artificially constructed metamaterials have attracted considerable interests because of their nontrivial and peculiar electromagnetic properties. Understanding nonlinear wave propagations in the systems are of importance, not only from the application, but also from the mathematical point of view. The minisymposium aims to bring together experts from the field of metamaterials and related areas, including but not limited to the creations and characteristics of localised structures in the systems. The target of the minisymposium is to present recent contributions to this subject, both theoretically and experimentally.

Organizer: Vassilis M. RothosAristotle University of Thessaloniki, Greece

Organizer: Hadi SusantoUniversity of Essex, United Kingdom

2:00-2:25 Pt-Symmetry and Embedded Modes in the Continuum for Magnetic MetamaterialsMario Molina, Universidad de Chile,

Chile

2:30-2:55 Quasi-Discrete Solitons in Nonlinear Transmission Line MetamaterialsD.J. Frantzeskakis, University of

Athens, Greece

3:00-3:25 Amplitude Modulation and Envelope Mode Formation in Left-Handed Media: a Survey of Recent ResultsIoannis Kourakis, Queen’s University,

Belfast, United Kingdom


MS62Connections Between Nonlinear Wave Equations and Geometry - Part II of III2:00 PM-4:00 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 1 see MS54 For Part 3 see MS70 This minisymposium will discuss some of the many facets of the interplay between geometry and nonlinear wave equations, and its increasingly important role in the study of nonlinear PDE and integrable systems, as well as differential and Poisson geometry. Topics will include geometric evolution equations---both continuous and discrete---arising in physical or geometric settings, geometric aspects of nonlinear wave equations (such as recursion operators and Poisson structures), and existence and construction of special solutions and coherent structures through geometric methods (e.g. Inverse Scattering Transform, Bäcklund transformations, algebro-geometric tools, Hirota method, etc.).




2:00-2:25 A Finite Dimensional Integrable System Arising in Shock ClusteringLuen-Chau Li, Pennsylvania State

University, USA

2:30-2:55 Multi-Component Integrable Wave Equations and Geometric Moving FramesStephen Anco, Brock University, Canada

3:00-3:25 Some Novel Geometric Realizations of Integrable HierarchiesThomas Ivey, College of Charleston, USA

3:30-3:55 Integrable Systems and Invariant Geometric Flows in Similarity Symplectic GeometryChangzheng Qu, Ningbo University, China


MS61Recent Advances in Numerical Methods for Shallow Water Equations and Related Models - Part I of II2:00 PM-4:00 PMRoom:Bevin Room - Wolfson Hall

For Part 2 see MS69 This minisymposium focuses on numerical methods for hyperbolic systems of conservation and balance laws used to model shallow water and related geophysical flows. Specific numerical difficulties different shallow water models have in common are due to the presence of(possibly singular) geometric source terms and/or nonconservative exchange terms. These may lead to the loss of hyperbolicity, nonlinear resonance, very complicated wave structures and, as a result, to appearance of spurious oscillations and slow convergence of numerical methods.Therefore development of highly accurate and efficient numerical methods for these systems is a very important and challenging task.

Organizer: Alina ChertockNorth Carolina State University, USA

Organizer: Alexander KurganovTulane University, USA

2:00-2:25 Well-Balanced Positivity Preserving Central-Upwind Scheme for the Shallow Water System with Friction TermsAlina Chertock, North Carolina State

University, USA

2:30-2:55 Well-Balanced Fully Coupled Central-Upwind Scheme for Shallow Water Flows over Erodible BedAbdolmajid Mohammadian and Xin Liu,

University of Ottawa, Canada

3:00-3:25 High Order Discontinuous Galerkin Methods for the Shallow Water EquationsYulong Xing, University of Tennessee and

Oak Ridge National Laboratory, USA

3:30-3:55 MLMC-FVM for Shallow Water Equations with Uncertain Bottom TopographyJonas Sukys, ETH Zürich, Switzerland


6:00-6:25 Multipole and Half-vortex Gap-solitons in Spin-orbit Coupled Bose-Einstein CondensatesYaroslav Kartashov, Institut de Ciències

Fotòniques, Spain; Vladimir V. Konotop, University of Lisbon, Portugal; Valery Lobanov, Institut de Ciències Fotòniques, Spain


MS64Nonlinear Waves, Singularities, and Collapses in Water Waves, Optics and Plasmas - Part III of IV4:30 PM-6:30 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS56 For Part 4 see MS72 Waves dynamics is one of the most interesting and appealing problems in applied mathematics and physics. In wast majority of interesting cases the problem of wave propagation can be solved not only in the linear approximation but also with nonlinear effects taken into account, due to powerful tools of modern applied mathematics and theoretical physics. Common approaches stimulate intensive interchange of ideas in the field which accelerates the development of the wave dynamics even further. Our minisymposium is devoted to new advances in the theory of waves and demonstrates vividly the similarity of approaches in a broad spectrum of important applications.



4:30-4:55 Wave Turbulence: A Story Far from OverAlan Newell, University of Arizona, USA

5:00-5:25 High-Frequency Instabilities of Small-Amplitude Solutions of Hamiltonian PDEsBernard Deconinck, University of

Washington, USA

5:30-5:55 Energy Growth in Switching Hamiltonian Systems of Fermi-Ulam TypeVadim Zharnitsky, University of Illinois,

USA; Maxim Arnold, University of Illinois at Urbana-Champaign, USA


CP9Geophysical Fluid Dynamics and Related Problems2:00 PM-4:00 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Bin Cheng, University of Surrey, United Kingdom

2:00-2:15 Time-Averaging and Error Estimates for Reduced Fluid Models.Bin Cheng, University of Surrey, United

Kingdom

2:20-2:35 Atmospheric Moisture Transport: Stochastic Dynamics of the Advection-Condensation EquationYue-Kin Tsang and Jacques Vanneste,

University of Edinburgh, United Kingdom

2:40-2:55 On the Asymptotics of Nonlinear Wall-Localized Thermal Convection WavesGeoffrey M. Vasil, University of Sydney,

Australia; Keaton Burns, Massachusetts Institute of Technology, USA

3:00-3:15 Optimal High-Order Diagonally-Implicit Runge-Kutta Schemes for Nonlinear Diffusive Systems on Atmospheric Boundary LayerFarshid Nazari and Abdolmajid

Mohammadian, University of Ottawa, Canada; Martin Charron and Ayrton Zadra, Environment Canada, Canada

3:20-3:35 Interaction of Atmospheric Vortex with A LandOlga S. Rozanova, Moscow State

University, Russia

3:40-3:55 Simulating Wall-Mode Convection: Numerical Techniques and First ResultsKeaton Burns, Massachusetts Institute of

Technology, USA; Geoffrey M. Vasil, University of Sydney, Australia




5:30-5:55 Hotspots in a Non-Local Crime ModelScott McCalla, University of California,

Los Angeles, USA; Jonah Breslau, Pomona College, USA; Sorathan Chaturapruek, Harvey Mudd College, USA; Theodore Kolokolnikov, Dalhousie University, Canada; Daniel Yazdi, University of California, Los Angeles, USA

6:00-6:25 Modeling Capillary OrigamiNicholas D. Brubaker, University of

Arizona, USA


MS66Analysis and Applications of Pattern-Forming Systems - Part I of II4:30 PM-6:30 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS74 This minisymposium will bring together eight researchers working on the underlying mathematical mechanisms which drive complexity in physical and biological systems. The significant applications to be addressed are crime modeling, elastic patterning and biological growth. A unifying feature in studies of these disparate applications is the need to apply and develop analytical tools for predicting the possible states of the underlying mathematical models. Significant challenges arise due to the highly non-linear and non-local nature of these models. Numerical simulations must also be carefully designed in order to preserve mathematical structures of the model.

Organizer: Alan E. LindsayUniversity of Notre Dame, USA

Organizer: Matthew PennybackerUniversity of New Mexico, USA

4:30-4:55 The Stability and Evolution of Curved Domains Arising from One Dimensional Localized PatternsAlan E. Lindsay, University of Notre

Dame, USA

5:00-5:25 Slowly Varying Control Parameters, Delayed Bifurcations, and the Stability of Spikes in Reaction-diffusion SystemsJustin C. Tzou, Dalhousie University,

Canada; Michael Ward, University of British Columbia, Canada; Theodore Kolokolnikov, Dalhousie University, Canada


MS65Spatial Localization: Recent Progress in Theory and Applications - Part I of II4:30 PM-6:30 PMRoom:Jock Colville Hall - Archives Center

For Part 2 see MS73 Spatially localized structures occur in many continuous dissipative systems and play an important role in their dynamics. They typically take the form of bound states of stationary or time-dependent fronts and have been observed in optics, biology and fluids. They are relevant to understanding the edge separating two stable states, such as laminar and turbulent shear flows. This minisymposium brings worldwide experts together to discuss and provide a summary of the recent progress in this area. The minisymposium is also of interest from a technical point of view as the investigation of spatial localization involves cutting-edge mathematical techniques.

Organizer: Cedric BeaumeUniversity of California, Berkeley, USA

4:30-4:55 Stability Properties of Localized Structures Near SnakingElizabeth J. Makrides and Bjorn Sandstede,


5:00-5:25 Dynamics of Cavity Solitons and Optical Frequency Combs in the Lugiato-Lefever EquationLendert Gelens, Stanford University, USA;

Pedro Parra-Rivas, Vrije Universiteit Brussel, Belgium; Damia Gomila, Universitat de les Illes Balears, Spain; François Leo, Ghent University, Belgium; Stéphane Coen, University of Auckland, New Zealand

5:30-5:55 Localised Hexagon Patches on the Surface of a Magnetic FluidDavid Lloyd, University of Surrey, United

Kingdom; Reinhard Richter, University of Bayreuth, Germany

6:00-6:25 Localized Solutions in Plane Couette Flow with RotationMatthew Salewski and Tobias Schneider,

Max Planck Institute for Dynamics and Self-Organization, Germany




MS68Algebraic Aspects of Integrable Systems and Applications - Part III of IV4:30 PM-6:30 PMRoom:Club Room - Concourse (1st Floor)

For Part 2 see MS60 For Part 4 see MS76 Integrable system has been studied extensively in related to many fields in both pure mathematics and applied mathematics. Meanwhile, the integrable system also promises applications ranging from water waves, nonlinear optics to numerical algorithms. The purpose of this special session is to bring together researchers from integrable system in both continuous and discrete integrable system to discuss recent advances on algebraic aspects of integrable systems and their applications.





4:30-4:55 A New Procedure to Approach Integrable DiscretizationXing-Biao Hu, Chinese Academy of

Sciences, China

5:00-5:25 Rogue Waves for Some Soliton EquationsYasuhiro Ohta, Kobe University, Japan

5:30-5:55 Complex and Coupled Complex Short Pulse Equations: Integrability, Discretization and Numerical SimulationsBao-Feng Feng, University of Texas - Pan

American, USA

6:00-6:25 New Results on the Explicit Monge-Taylor Forms for Submanifolds Under Group Actions Using Equivariant Moving Frame MethodRuoxia Yao, Shaanxi Normal University,

China

5:30-5:55 Time Domain Nonlinear Structures and Substructures for Ultrafast PhotonicsLevon Mouradian, Aram Zeytunyan,

Hrach Toneyan, and Garegin Yesayan, Yerevan State University, Armenia; Ruben Zadoyan, Newport Corporation, USA; Frédéric Louradour and Alain Barthélémy, Université de Limoges, France

6:00-6:25 Mechanisms and Definitions of Rogue Waves in Nonlinear SystemsJohn Dudley, Université de Franche-Comté,

France; Goery Genty, Tampere University of Technology, Finland; Frederic Dias, University College Dublin, Ireland


MS67Nonlinear Coherent Structures in Photonics - Part I of III4:30 PM-6:30 PMRoom:Recital Room - Music Center

For Part 2 see MS75 Nature provides numerous examples of coherent nonlinear structures and waves. Often, physical systems sharing the same underlying nonlinear phenomenon can be modelled by similar equations, allowing for cross- disciplinary exchange of ideas and methods. This minisymposium, focused on coherent structures in photonics, brings together a number of leading experts in various aspects of nonlinear optical waves. The minisymposium scope covers both fundamental and applied nonlinear photonics with topics including temporal and spatial nonlinear effects, ultrafast processes, solitons and rogue waves, pulse shaping and generation, nonlinearity in nanophotonics, wave propagation and localization in disordered media, and fibre lasers.

Organizer: Sonia BoscoloAston University, United Kingdom

Organizer: Sergei TuritsynAston University, United Kingdom

4:30-4:55 In-Cavity Transformations for New Nonlinear Regimes of Pulse Generation in Mode-Locked Fibre LasersSonia Boscolo and Sergei K. Turitsyn,

Aston University, United Kingdom; Christophe Finot, Université de Bourgogne, France

5:00-5:25 Nonlinear Pulse Shaping in Normally Dispersive Fibres: Experimental ExamplesKamal Hammani, Julien Fatome, and

Guy Millot, Université de Bourgogne, France; Sonia Boscolo, Aston University, United Kingdom; Hervé Rigneault, Institut Fresnel, France; Stefano Wabnitz, University of Brescia, Italy; Christophe Finot, Université de Bourgogne, France




MS71Coherent Structures in Nonlinear Hamiltonian Lattices: OPEN PROBLEMS4:30 PM-6:30 PMRoom:JCR Games Room – Concourse (Ground Floor)

Hamiltonian lattices are ubiquitous in many branches of physics and materials science, and the standard equations (FPU-type chains, Klein-Gordon lattices, discrete nonlinear Schroedinger equations) have attracted a lot of interest in different communities. The last decades have seen a dramatic progress in the mathematical analysis of coherent structures in such systems but many fundamental problems remain unsolved. Moreover, new questions and problems constantly arise from the ongoing research activities. This minisymposium focuses on open problems and intends to provide a forum for discussing the current state and the future development of the research field.

Organizer: Ioannis GiannoulisUniversity of Ioannina, Greece

Organizer: Michael HerrmannSaarland University, Germany

4:30-4:55 Localized Waves in Fully Nonlinear MediaGuillaume James, Université de

Grenoble and CNRS, France

5:00-5:25 Breathers in Two-dimensional Fermi-Pasta-Ulam LatticesJonathan Wattis, University of

Nottingham, United Kingdom

5:30-5:55 New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova ChainPhoebus Rosakis, University of Crete,

Greece

6:00-6:25 On the Travelling Wave Problem for Phase Transitions in the Fermi-Pasta-Ulam ChainHartmut Schwetlick, University of Bath,

United Kingdom


MS70Connections Between Nonlinear Wave Equations and Geometry - Part III of III4:30 PM-6:30 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 2 see MS62 This minisymposium will discuss some of the many facets of the interplay between geometry and nonlinear wave equations, and its increasingly important role in the study of nonlinear PDE and integrable systems, as well as differential and Poisson geometry. Topics will include geometric evolution equations---both continuous and discrete---arising in physical or geometric settings, geometric aspects of nonlinear wave equations (such as recursion operators and Poisson structures), and existence and construction of special solutions and coherent structures through geometric methods (e.g. Inverse Scattering Transform, Bäcklund transformations, algebro-geometric tools, Hirota method, etc.).




4:30-4:55 Closed Form Solutions of the Hirota EquationCornelis Van der Mee, Universita di

Cagliari, Italy

5:00-5:25 Integrable Nature of Modulational InstabilityGino Biondini and Emily Fagerstrom, State

University of New York, Buffalo, USA

5:30-5:55 On the Spectrum of the Defocusing NLS Equation with Non-zero Boundary ConditionsBarbara Prinari, University of Colorado,

Colorado Springs, USA; Gino Biondini, State University of New York, Buffalo, USA

6:00-6:25 Rational Solitons of Wave Resonant-Interaction ModelsSara Lombardo, Northumbria University,

United Kingdom; Antonio Degasperis, Università La Sapienza, Rome, Italy


MS69Recent Advances in Numerical Methods for Shallow Water Equations and Related Models - Part II of II4:30 PM-6:30 PMRoom:Bevin Room - Wolfson Hall

For Part 1 see MS61 This minisymposium focuses on numerical methods for hyperbolic systems of conservation and balance laws used to model shallow water and related geophysical flows. Specific numerical difficulties different shallow water models have in common are due to the presence of(possibly singular) geometric source terms and/or nonconservative exchange terms. These may lead to the loss of hyperbolicity, nonlinear resonance, very complicated wave structures and, as a result, to appearance of spurious oscillations and slow convergence of numerical methods.Therefore development of highly accurate and efficient numerical methods for these systems is a very important and challenging task.

Organizer: Alina ChertockNorth Carolina State University, USA

Organizer: Alexander KurganovTulane University, USA

4:30-4:55 RVM Finite Volume Methods: Applications to Multilayer Shallow FlowsJose M. Gallardo and Manuel Castro,

University of Malaga, Spain; Antonio Marquina, University of Valencia, Spain

5:00-5:25 Well-Balanced Ale: a Dynamic Mesh Adaptation Strategy for Shallow Water FlowsMario Ricchiuto, INRIA, France

5:30-5:55 Well-Balanced Positivity Preserving Cell-Vertex Central-Upwind Scheme for Shallow Water FlowsAbdelaziz Beljadid, University of Ottawa,

Canada

6:00-6:25 Path-Conservative Central-Upwind Schemes for Nonconservative Hyperbolic SystemsAlexander Kurganov, Tulane University,

USA


Thursday, August 14


Thursday, August 14

MS72Nonlinear Waves, Singularities, and Collapses in Water Waves, Optics and Plasmas - Part IV of IV8:10 AM-10:10 AMRoom:Wolfson Auditorium - Wolfson Hall

For Part 3 see MS64 Waves dynamics is one of the most interesting and appealing problems in applied mathematics and physics. In wast majority of interesting cases the problem of wave propagation can be solved not only in the linear approximation but also with nonlinear effects taken into account, due to powerful tools of modern applied mathematics and theoretical physics. Common approaches stimulate intensive interchange of ideas in the field which accelerates the development of the wave dynamics even further. Our minisymposium is devoted to new advances in the theory of waves and demonstrates vividly the similarity of approaches in a broad spectrum of important applications.




SIAG/NWCS Business Meeting8:00 PM-8:45 PMRoom:Wolfson Auditorium - Wolfson Hall

(Open to SIAG/NWCS members)

Complimentary beer and wine will be served.


CP10Fluid Dynamics and Related Problems II4:30 PM-6:10 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Matthew R. Turner, University of Surrey, United Kingdom

4:30-4:45 Fluid Ratcheting by Oscillating Channel Walls with SawteethJie Yu, North Carolina State University,

USA

4:50-5:05 Diffraction and Reflection of a Weak Shock at a Right-Angled Wedge in Real FluidsNeelam Gupta, Indian Institute of

Technology-Bombay, India

5:10-5:25 Nonlinear Energy Transfer Between Fluid Sloshing and Vessel MotionMatthew R. Turner, Tom J. Bridges, and

Hamid Alemi Ardakani, University of Surrey, United Kingdom

5:30-5:45 A Theory of Weakly Non-Linear DetonationsLuiz Faria and Aslan R. Kasimov, King

Abdullah University of Science & Technology (KAUST), Saudi Arabia; Rodolfo R. Rosales, Massachusetts Institute of Technology, USA

5:50-6:05 Pattern Formation in a Circular Hydraulic JumpAslan R. Kasimov, King Abdullah

University of Science & Technology (KAUST), Saudi Arabia

Dinner Break6:30 PM-8:00 PMAttendees on their own.




Thursday, August 14

MS74Analysis and Applications of Pattern-Forming Systems - Part II of II8:10 AM-9:40 AMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 1 see MS66 This minisymposium will bring together eight researchers working on the underlying mathematical mechanisms which drive complexity in physical and biological systems. The significant applications to be addressed are crime modeling, elastic patterning and biological growth. A unifying feature in studies of these disparate applications is the need to apply and develop analytical tools for predicting the possible states of the underlying mathematical models. Significant challenges arise due to the highly non-linear and non-local nature of these models. Numerical simulations must also be carefully designed in order to preserve mathematical structures of the model.

Organizer: Alan E. LindsayUniversity of Notre Dame, USA

Organizer: Matthew PennybackerUniversity of New Mexico, USA

8:10-8:35 Pattern-Forming Fronts in PhyllotaxisMatthew Pennybacker, University of

New Mexico, USA

8:40-9:05 Isometric Immersions and Pattern Formation in Non-Euclidean Elastic SheetsJohn A. Gemmer, Brown University,

USA; Shankar C. Venkataramani, University of Arizona, USA

9:10-9:35 Nanoscale Pattern Formation by Ion Bombardment of Binary CompoundsPatrick Shipman, Colorado State

University, USA

Thursday, August 14

MS73Spatial Localization: Recent Progress in Theory and Applications - Part II of II8:10 AM-10:10 AMRoom:Jock Colville Hall - Archives Center

For Part 1 see MS65 Spatially localized structures occur in many continuous dissipative systems and play an important role in their dynamics. They typically take the form of bound states of stationary or time-dependent fronts and have been observed in optics, biology and fluids. They are relevant to understanding the edge separating two stable states, such as laminar and turbulent shear flows. This minisymposium brings worldwide experts together to discuss and provide a summary of the recent progress in this area. The minisymposium is also of interest from a technical point of view as the investigation of spatial localization involves cutting-edge mathematical techniques.

Organizer: Cedric BeaumeUniversity of California, Berkeley, USA

8:10-8:35 Localised Solutions in Integral Neural Field EquationsDaniele Avitabile, University of

Nottingham, United Kingdom

8:40-9:05 Localized Convection in a Rotating Fluid LayerCedric Beaume, University of California,

Berkeley, USA

9:10-9:35 Steady and Oscillatory Localised States in Boussinesq MagnetoconvectionPaul J. Bushby and Matthew Buckley,

Newcastle University, United Kingdom

9:40-10:05 Moving Localized Structures in a Doubly Diffusive SystemDavid Lo Jacono and Alain Bergeon,

Universite de Toulouse, France; Edgar Knobloch, University of California, Berkeley, USA

8:10-8:35 Solitons, Self-Induced Transparency, and Quantum Cascade LasersCurtis R. Menyuk, University of Maryland,

Baltimore County, USA; Muhammad Talukder, Bangladesh University of Engineering & Technology, Bangladesh

8:40-9:05 Thresholds and Blow-up Dynamics in the Nonlinear Dispersive EquationsSvetlana Roudenko, George Washington

University, USA

9:10-9:35 On Multi-Dimensional Compact PatternsPhilip Rosenau, Tel Aviv University, Israel

9:40-10:05 Branch Cut Singularity of Stokes WavePavel M. Lushnikov, University of New

Mexico, USA


Thursday, August 14

MS76Algebraic Aspects of Integrable Systems and Applications - Part IV of IV8:10 AM-10:10 AMRoom:Club Room - Concourse (1st Floor)

For Part 3 see MS68 Integrable system has been studied extensively in related to many fields in both pure mathematics and applied mathematics. Meanwhile, the integrable system also promises applications ranging from water waves, nonlinear optics to numerical algorithms. The purpose of this special session is to bring together researchers from integrable system in both continuous and discrete integrable system to discuss recent advances on algebraic aspects of integrable systems and theirs applications.





8:10-8:35 General Solutions of Arbitraray First Order Autonomous PDEsSenyue Lou, Ningbo University, China

8:40-9:05 On Nonintegrable Semidiscrete Hirota Equation: Gauge Equivalent Structures and Dynamical PropertiesZuonong Zhu, Shanghai Jiao Tong

University, China

9:10-9:35 Invariant Manifold of the KdV EquationYong Chen and Yuqi Li, Eastern China

Normal University, China; Senyue Lou, Ningbo University, China

9:40-10:05 KP Web-solitons from Wave PatternsSarbarish Chakravarty, University of

Colorado, Colorado Springs, USA

Stefan Wabnitz, University of Brescia, Italy

9:10-9:35 Transverse Disorder-Induced Localizations in Nonlocal Nonlinear Media: Theory and ExperimentsClaudio Conti, Università degli Studi di

Roma, La Sapienza, Italy; Viola Folli, Universita di Roma “La Sapienza,” Italy; Marco Leonetti, Università degli Studi di Roma, La Sapienza, Italy; Salman Karbasi and Arash Mafi, University of Wisconsin, Milwaukee, USA

9:40-10:05 Optical Wave Turbulence: Toward a Unified Non-Equilibrium Thermodynamic Description of Statistical Nonlinear OpticsGang Xu, University of Burgundy, France;

Josselin Garnier, Universite Paris 7-Denis Diderot, France; Stefano Trillo, University of Ferrara, Italy; Antonio Picozzi, Université de Bourgogne, France

Thursday, August 14

MS75Nonlinear Coherent Structures in Photonics - Part II of III8:10 AM-10:10 AMRoom:Recital Room - Music Center

For Part 1 see MS67 For Part 3 see MS83 Nature provides numerous examples of coherent nonlinear structures and waves. Often, physical systems sharing the same underlying nonlinear phenomenon can be modelled by similar equations, allowing for cross- disciplinary exchange of ideas and methods. This minisymposium, focused on coherent structures in photonics, brings together a number of leading experts in various aspects of nonlinear optical waves. The minisymposium scope covers both fundamental and applied nonlinear photonics with topics including temporal and spatial nonlinear effects, ultrafast processes, solitons and rogue waves, pulse shaping and generation, nonlinearity in nanophotonics, wave propagation and localization in disordered media, and fibre lasers.



8:10-8:35 Relative Intensity Noise Transfer in Second-Order Raman Amplification with Random Distributed Feedback Ultra-Long Fibre LasersJavier Nuno, CSIC, Madrid, Spain; Juan

Diego Ania Castañón, Instituto de Óptica (CSIC), Madrid, Spain

8:40-9:05 Order and Chaos in Fibre Lasers



9:10-9:35 Coherent Structures Interaction and Self-Organization in Dissipative TurbulenceSerafim Kalliadasis and Marc Pradas,

Imperial College London, United Kingdom; Te-Sheng Lin and Dmitri Tseluiko, Loughborough University, United Kingdom

9:40-10:05 Waves on the Interface of Two-Layer Liquid System Subject to Longitudinal Vibrations: Stability and Collision of SolitonsDenis S. Goldobin, Russian Academy

of Sciences, Russia; Kseniya Kovalevskaya, Pennsylvania State University, USA

Thursday, August 14

MS78Nonlinear Waves and Patterns Generated by Instabilities - Part I of II8:10 AM-10:10 AMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 2 see MS86 The phenomenon of the pattern formation has been extensively studied during several decades. The major success has been achieved in the exploration of patterns governed by some versions of the Ginzburg-Landau equation. However, there exists a variety of problems where the Ginzburg-Landau equation is not efficient. The present minisymposium exposes recent achievements in the field of nonlinear waves and patterns created by instabilities, which need diverse tools for their description. The list of problems includes instabilities developed under the action of vibration and modulation of parameters, waves generated by rotation, different aspects of the nonlinear film dynamics, and the dynamics of coherent structures in dissipative turbulence.

Organizer: Alexander NepomnyashchyTechnion - Israel Institute of Technology, Israel

Organizer: Sergey ShklyaevInstitute of Continuous Media Mechanics, Perm, Russia

8:10-8:35 Symmetries and Parametric Instabilities in Vibrating ContainersJose Manuel Vega, Universidad

Politécnica de Madrid, Spain

8:40-9:05 Modulation of a Heat Flux in a Layer of Binary MixtureIrina Fayzrakhmanova, Perm State

Humanitarian Pedagogical University, Perm, Russia; Sergey Shklyaev, Institute of Continuous Media Mechanics, Perm, Russia; Alexander Nepomnyashchy, Technion Israel Institute of Technology, Israel

Thursday, August 14

MS77Discrete and Continuous Nonlocal Wave Equations and Applications - Part I of III8:10 AM-10:10 AMRoom:Bevin Room - Wolfson Hall

For Part 2 see MS85 The session focuses on recent results on nonlinear wave equations with nonlocal terms, including dispersive wave equations coupled with elliptic or parabolic equations. Applications include nonlinear optics in thermal media, water wave models, and coupled nonlinear lattice models. The inclusion of nonlocal terms can produce subtle and physically important effects in the properties of coherent structures, and requires more general analytical and numerical tools. The session will include works motivated by recent experimental studies, as well as more theoretical results on the relevant models.

Organizer: Panayotis PanayotarosIIMAS-UNAM, Mexico

Organizer: Richard O. MooreNew Jersey Institute of Technology, USA

8:10-8:35 Dynamics of Localized Solution in Nonlocal NLS Equation with Double Well PotentialVassilis M. Rothos, Aristotle University of

Thessaloniki, Greece

8:40-9:05 Surface Signature of Internal WavesPhilippe Guyenne, University of Delaware,

USA

9:10-9:35 The Role of Radiation Loss in the Evolution of Elliptic Solitons in Nonlocal Soft MediaLuke Sciberras, Universidad Nacional

Autónoma de México, Mexico

9:40-10:05 Mobile Localized Solutions for An Electron in Lattices with Dispersive and Non-Dispersive PhononsLuis Cisneros, Instituto Politécnico

Nacional, Mexico



Thursday, August 14Remarks10:40 AM-10:45 AMRoom:Wolfson Auditorium - Wolfson Hall

IP7Momentum Maps, Shape Analysis and Solitons10:45 AM-11:30 AMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Sheehan Olver, University of Sydney, Australia

Much of this talk is based on work done with Jerry Marsden (1942 - 2010) on shared geometric properties in the analysis of fluid flow and shape transformations. The talk will discuss uses of geometric mechanics in the problem of registration of images, primarily in the example of planar closed curves. Many types of mathematics apply in this problem, including soliton theory and momentum maps. Some trade secrets will be revealed.

Darryl D. HolmImperial College London, United Kingdom and Los Alamos National Laboratory, USA



Thursday, August 14

CP11Surface Waves and Related Problems8:10 AM-10:10 AMRoom:Tizard Room - Concourse (1st Floor)

Chair: David I. Ketcheson, King Abdullah University of Science & Technology (KAUST), Saudi Arabia

8:10-8:25 On Periodic Solutions of a Model Equation for Surface Waves of Moderate Amplitude in Shallow WaterNilay Duruk Mutlubas, Istanbul

Kemerburgaz University, Turkey

8:30-8:45 Solitary Waves Without Dispersive Terms: the Shallow Water Equations over a Periodic BottomDavid I. Ketcheson, King Abdullah

University of Science & Technology (KAUST), Saudi Arabia; Manuel Quezada De Luna, Texas A&M University, USA

8:50-9:05 High Order Hamiltonian Water Wave Models with Wave-Breaking MechanismRuddy Kurnia and E. Van Groesen,

University of Twente, The Netherlands

9:10-9:25 Interaction of Strongly Nonlinear Waves on the Free Surface of Non-Conducting Fluid under the Action of Horizontal Electric FieldEvgeny Kochurin and Nikolay Zubarev,

Russian Academy of Sciences, Russia

9:30-9:45 The Higher-Order Boussinesq Equation with Periodic Boundary Conditions: Analytical and Numerical ResultsGoksu Topkarci and Gulcin M. Muslu,

Istanbul Technical University, Turkey; Handan Borluk, Isik University, Turkey

9:50-10:05 Ocean Wave Energy Potential and MicroseismsPaul Christodoulides, Cyprus University

of Technology, Cyprus; Lauranne Pellet, École Centrale de Marseille, France; Frédéric Dias, University College Dublin, Ireland and Ecole Normale Supérieure de Cachan, France


Thursday, August 14

MS79Model Reduction for Complex Systems Exhibiting Wave Phenomena8:10 AM-10:10 AMRoom:JCR Games Room – Concourse (Ground Floor)

The study of complex systems equations and large systems of ordinary differential equations is important in many problems from fluid mechanics, climate, nonlinear optics, molecular dynamics, etc. The complexity can come from the number of fields involved or the underlying geometry. An example is the propagation of waves on networks. For this study, it is important to be able to reduce the complexity and obtain simpler equations that can be studied analytically. This reduction can be done by projecting on coherent structures or on linear modes. We present works that use both approaches and compare them on large systems of coupled differential equations and of coupled partial differential equations.

Organizer: Brenton J. LeMesurierCollege of Charleston, USA

Organizer: Alejandro AcevesSouthern Methodist University, USA

Organizer: Jean-Guy CaputoUniversite de Rouen, France

8:10-8:35 Model Reduction in Optics and Traffic ModelingMads Sørensen, Technical University of

Denmark, Denmark

8:40-9:05 Model Reduction for Waves in NetworksJean-Guy Caputo, Universite de Rouen,

France

9:10-9:35 Disorder in One-Dimensional Granular CrystalsAlejandro J. Martinez, University of

Oxford, United Kingdom

9:40-10:05 Partial Continuum Limits for Exciton Pulses in Large MoleculesBrenton J. LeMesurier, College of

Charleston, USA


Thursday, August 14

MS81Nonlinear Waves in Fluid Flows and Their Interaction with Structures - Part I of II2:00 PM-4:00 PMRoom:Jock Colville Hall - Archives Center

For Part 2 see MS89 This session focuses on nonlinear waves in fluid flows and their interaction with structures. Examples include internal and surface waves in the ocean, flexural-gravity waves in floating ice sheets, and hydroelastic waves in industrial or biological fluid systems. Such problems are typically described by nonlinear dispersive PDEs with coupling terms, which require sophisticated analytical techniques and accurate numerical methods to calculate such solutions as solitary waves, breaking waves or waves with a multivalued profile. This session will feature a wide range of talks on the mathematical modeling, numerical simulation and laboratory experiment of such waves.

Organizer: Philippe GuyenneUniversity of Delaware, USA

Organizer: Emilian I. ParauUniversity of East Anglia, United Kingdom

2:00-2:25 Experimental Observation of Unstable Mode 2 Internal WavesMagda Carr, University of St. Andrews,

United Kingdom; Peter A Davies, University of Dundee, Scotland; Ruud Hoebers, Eindhoven University of Technology, Netherlands

2:30-2:55 Comparing Stokes Drift for Internal and Surface Gravity Wave PacketsTon van den Bremer and Paul Taylor,

University of Oxford, United Kingdom; Bruce Sutherland, University of Alberta, Canada

3:00-3:25 Analysis and Computations of the Initial Value Problem for Hydroelastic WavesMichael Siegel, New Jersey Institute of

Technology, USA

3:30-3:55 Hydraulic Falls Under a Floating Ice PlateCharlotte Page and Emilian I. Parau,


Thursday, August 14

MS80The Hamiltonian and Symplectic Methods in the Theory of Non-Linear Waves - Part I of II2:00 PM-4:00 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 2 see MS88 Hamitonian structures have played a central role in the theory of nonlinear waves. Historically they played an abstract role, but increasingly they are viewed as practical tools for solving open problems in the theory of nonlinear waves. The subject is ever expanding, and the purpose of this minisymposium is to present a snapshot of recent developments. Topics include Hamiltonian structures of nonlinear dispersive wave equations, theory of Hamiltonian PDEs, Krein signature, the Maslov index, stability of solitary waves (symplectic Evans function, the energy-momentum method), multi-symplectic structures, averaged Lagrangians, Whitham modulation theory, and numerical methods for all of the above.

Organizer: Frederic ChardardUniversite Jean Monnet, France

Organizer: Tom J. BridgesUniversity of Surrey, United Kingdom

2:00-2:25 Transversality of Solitary Waves and Their StabilityFrederic Chardard, Universite Jean

Monnet, France

2:30-2:55 An Application of Maslov Index to the Stability Analysis for Standing PulsesChiao-Nen Chen, National Changhua

University of Education, Taiwan

3:00-3:25 Stability of Periodic Waves in Hamiltonian PdesMiguel Rodrigues, University of Lyon 1,

France

3:30-3:55 Sloshing Dynamics with the Hamiltonian Particle-mesh MethodHamid Alemi Ardakani, Tom J. Bridges,

and Matthew R. Turner, University of Surrey, United Kingdom

Thursday, August 14

IP8Symmetry, Modulation and Nonlinear Waves1:00 PM-1:45 PMRoom:Wolfson Auditorium - Wolfson Hall

Chair: Barbara Prinari, University of Colorado, Colorado Springs, USA

Modulation underpins many facets of the analysis of nonlinear waves and patterns. A new perspective on modulation combined with symmetry and conservation laws will be presented, which leads to a mechanism for the emergence of model wave PDEs such as KdV, KP, Boussinesq and others. This combination results in simple geometric formulae for the coefficients. Generalizations to multi-phase wavetrains, systems of conservation laws, Whitham equations with dispersion, and a mechanism for the formation of multi-pulse planforms in pattern formation will also be presented.

Tom J. BridgesUniversity of Surrey, United Kingdom



3:00-3:25 Self-Tuning Nonlinear Optical SystemsJ. Nathan Kutz, Steven Bruton, and Xing

Fu, University of Washington, USA

3:30-3:55 Thermo-Optical Effects and Mode Instabilities in Large Mode Area Photonic Crystal FibersAnnamaria Cucinotta, Universita degli

Studi di Parma, Italy; Enrico Coscelli, Federica Poli, and Stefano Selleri, University of Parma, Italy

Thursday, August 14

MS83Nonlinear Coherent Structures in Photonics - Part III of III2:00 PM-4:00 PMRoom:Recital Room - Music Center

For Part 2 see MS75 Nature provides numerous examples of coherent nonlinear structures and waves. Often, physical systems sharing the same underlying nonlinear phenomenon can be modelled by similar equations, allowing for cross- disciplinary exchange of ideas and methods. This minisymposium, focused on coherent structures in photonics, brings together a number of leading experts in various aspects of nonlinear optical waves. The minisymposium scope covers both fundamental and applied nonlinear photonics with topics including temporal and spatial nonlinear effects, ultrafast processes, solitons and rogue waves, pulse shaping and generation, nonlinearity in nanophotonics, wave propagation and localization in disordered media, and fibre lasers.



2:00-2:25 Tuning of Surface Plasmon Polaritons Beat Length in Graphene Directional CouplersCostantino De Angelis, Aldo Auditore,

and Andrea Locatelli, University of Brescia, Italy; Alejandro Aceves, Southern Methodist University, USA

2:30-2:55 Ultrafast Spatial and Temporal Soliton Dynamics in Gas-Filled Hollow-Core Photonic Crystal FibresJohn Travers, Francesco Tani, Ka Fai Mak,

Philipp Hölzer, Alexey Ermolov, and Philip Russell, Max Planck Institute for the Science of Light, Germany

Thursday, August 14

MS82Dynamical Systems and Climate - Part I of II2:00 PM-4:00 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 2 see MS90 Over the past few decades it has become apparent that the Earth’s climate is a rich source of applied mathematical problems, particularly in the fields of dynamical systems and data assimilation. The rigorous study of conceptual models has provided new insight into climate dynamics, along the way necessitating the development of exciting new mathematical tools. This minisymposium will focus on the application of dynamical methods to problems in such diverse areas as data assimilation, desertification, and ocean circulation, with an emphasis on the unique mathematical challenges arising in such studies.

Organizer: Graham CoxUniversity of North Carolina, Chapel Hill, USA

Organizer: Thomas BellskyArizona State University, USA

2:00-2:25 Stablility of Localized Structure for a Semi-Arid Climate ModelThomas Bellsky, Arizona State

University, USA

2:30-2:55 Semi-Strong Desertification Dynamics with a Slowly Changing ParameterEric Siero and Arjen Doelman, Leiden

University, Netherlands; Thomas Bellsky, Arizona State University, USA

3:00-3:25 Tipping and Warning Signs for Patterns and Propagation Failure in SPDEsKarna V. Gowda, Northwestern

University, USA; Christian Kuehn, Vienna University of Technology, Austria

3:30-3:55 Model Reduction and Response for Two-Timescale Systems Using Fluctuation-DissipationMarc Kjerland, University of Illinois,

Chicago, USA



Thursday, August 14

MS85Discrete and Continuous Nonlocal Wave Equations and Applications - Part II of III2:00 PM-3:30 PMRoom:Bevin Room - Wolfson Hall

For Part 1 see MS77 For Part 3 see MS93 The session focuses on recent results on nonlinear wave equations with nonlocal terms, including dispersive wave equations coupled with elliptic or parabolic equations. Applications include nonlinear optics in thermal media, water wave models, and coupled nonlinear lattice models. The inclusion of nonlocal terms can produce subtle and physically important effects in the properties of coherent structures, and requires more general analytical and numerical tools. The session will include works motivated by recent experimental studies, as well as more theoretical results on the relevant models.



2:00-2:25 Exact and Approximate Solutions for Solitary Waves in Nematic Liquid CrystalsMichael MacNeil, University of

Edinburgh, United Kingdom

2:30-2:55 Controlability of Schroedinger Equation with a Hartree Type NonlinearityMariano De Leo, Universidad Nacional

General Sarmiento, Argentina

3:00-3:25 Localized Solutions and Traveling Waves in a Nonlocal Parametrically Forced Nonlinear Schroedinger EquationRichard O. Moore, New Jersey Institute

of Technology, USA

3:00-3:25 Standing Waves and Heteroclinic Networks in the Nonlocal Complex Ginzburg-Landau Equation for Electrochemical SystemsVladimir Garcia-Morales, Technische

Universität München, Germany

3:30-3:55 Coherent Structures in Confined Swarming FlowsFranck Plouraboue, CNRS, France;

Adama Creppy and Olivier Praud, Toulouse University, France; Pierre Degond, Imperial College London, United Kingdom; Hui Yu, Universite de Toulouse, France; Nan Wang, National University of Singapore, Singapore

Thursday, August 14

MS84Coherent Structures Driven by Coulombic and Other Long Range Interactions - Part I of II2:00 PM-4:00 PMRoom:Club Room - Concourse (1st Floor)

For Part 2 see MS92 Coherent structures (CSs) are fundamental in pattern forming systems, e.g., reaction-diffusion systems, convection, and periodically forced media. Recently, evidences of CSs are also being emerged in systems related to renewable energy devices, e.g., membranes in fuel cells, batteries, and ionic liquids. Such systems extend the reaction-diffusion type systems to incorporate effects like Coulombic interactions and global conservations. The minisymposium goals: (1) to survey the development of models and analysis methods that give rise to CSs and (2) to scrutinize the connections between models and their impacts to real life applications, e.g. renewable energy devices, polymer based media and vegetation.

Organizer: Arik YochelisBen Gurion University Negev, Israel

Organizer: Nir GavishTechnion - Israel Institute of Technology, Israel

2:00-2:25 On Electrical Diffuse Layers in Ionic Liquids and Heteroclinic-Type ConnectionsArik Yochelis, Ben Gurion University

Negev, Israel

2:30-2:55 Bifurcations in the Langmuir-Blodgett Transfer ProblemMichael H. Koepf, Ecole Normale

Supérieure, France; Uwe Thiele, University of Muenster, Germany



Thursday, August 14

MS87Stratified Fluids, Coherent Structures, and Their Interactions - Part I of II2:00 PM-4:00 PMRoom:JCR Games Room – Concourse (Ground Floor)

For Part 2 see MS94 Fluid-structure interactions are ubiquitous in fluid mechanics. The presence of ambient fluid stratification can increase the level of complexity and provide a rich parametric space with new and interesting effects. In this minisymposium, presenters will discuss the dynamics of fluid-structure interactions and multiphase flow in homogeneous and stratified settings. They will explore the resulting fluid flow and emergence of coherent structures in physically relevant problems which pose challenging mathematical questions, including handling varying boundary conditions in the flow. Studies will draw from all aspects of scientific investigations in this area, from experimental, to analytical and numerical results.

Organizer: Shilpa KhatriUniversity of North Carolina, Chapel Hill, USA

Organizer: Roberto CamassaUniversity of North Carolina, Chapel Hill, USA

Organizer: Richard McLaughlinUniversity of North Carolina, Chapel Hill, USA

2:00-2:25 Experiments and Theory for Porous Spheres Settling in Sharply Stratified FluidsShilpa Khatri, Roberto Camassa, Richard

McLaughlin, Jennifer Prairie, Brian White, and Sungduk Yu, University of North Carolina, Chapel Hill, USA

3:00-3:25 Continuously Quenched Pattern Dynamics in Drying Liquid FilmsPierre Colinet, Université Libre de

Bruxelles, Belgium

3:30-3:55 Compactons Induced by Nonconvex AdvectionAlex Oron, Technion - Israel Institute of

Technology, Israel; Philip Rosenau, Tel Aviv University, Israel

Thursday, August 14

MS86Nonlinear Waves and Patterns Generated by Instabilities - Part II of II2:00 PM-4:00 PMRoom:Cockcroft Room - Concourse (Ground Floor)

For Part 1 see MS78 The phenomenon of the pattern formation has been extensively studied during several decades. The major success has been achieved in the exploration of patterns governed by some versions of the Ginzburg-Landau equation. However, there exists a variety of problems where the Ginzburg-Landau equation is not efficient. The present minisymposium exposes recent achievements in the field of nonlinear waves and patterns created by instabilities, which need diverse tools for their description. The list of problems includes instabilities developed under the action of vibration and modulation of parameters, waves generated by rotation, different aspects of the nonlinear film dynamics, and the dynamics of coherent structures in dissipative turbulence.

Organizer: Alexander NepomnyashchyTechnion - Israel Institute of Technology, Israel

Organizer: Sergey ShklyaevInstitute of Continuous Media Mechanics, Perm, Russia

2:00-2:25 Thin Film Flows over Spinning Discs: Numerical Simulation of Three-Dimensional WavesOmar K. Matar, Imperial College

London, United Kingdom

2:30-2:55 Wave Instability of a Rotating Liquid-Liquid InterfaceNikolay Kozlov, Anastasiia Kozlova,

and Darya Shuvalova, Perm State Humanitarian Pedagogical University, Perm, Russia

continued in next column continued on next page


Thursday, August 14

MS88The Hamiltonian and Symplectic Methods in the Theory of Non-Linear Waves - Part II of II4:30 PM-6:30 PMRoom:Wolfson Auditorium - Wolfson Hall

For Part 1 see MS80 Hamitonian structures have played a central role in the theory of nonlinear waves. Historically they played an abstract role, but increasingly they are viewed as practical tools for solving open problems in the theory of nonlinear waves. The subject is ever expanding, and the purpose of this minisymposium is to present a snapshot of recent developments. Topics include Hamiltonian structures of nonlinear dispersive wave equations, theory of Hamiltonian PDEs, Krein signature, the Maslov index, stability of solitary waves (symplectic Evans function, the energy-momentum method), multi-symplectic structures, averaged Lagrangians, Whitham modulation theory, and numerical methods for all of the above.

Organizer: Frederic ChardardUniversite Jean Monnet, France

Organizer: Tom J. BridgesUniversity of Surrey, United Kingdom

4:30-4:55 A Hamiltonian Analogue of the Meandering TransitionClaudia Wulff, University of Surrey,

United Kingdom

5:00-5:25 Dispersive Shear Shallow Water FlowsSergey Gavrilyuk, University of Aix-

Marseille, France

5:30-5:55 Standing Pulse Solution of Fitzhugh-Nagumo EquationsYung-Sze Choi, University of

Connecticut, USA

6:00-6:25 Multisymplectic Structure and the Stability of Solitary WavesTom J. Bridges, University of Surrey,

United Kingdom

Thursday, August 14

CP12Bose-Einstein, Nonlinear Optics and Related Problems2:00 PM-4:00 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Dmitri Tseluiko, Loughborough University, United Kingdom

2:00-2:15 A Multiscale Continuation Algorithm for Binary Rydberg-Dressed Bose-Einstein CondensatesCheng-Sheng Chien, Chien Hsin University

of Science and Technology, Taiwan; Sirilak Sriburadet, National Chung-Hsing University, Taiwan; Yun-Shih Wang, Chien Hsin University of Science and Technology, Taiwan

2:20-2:35 Vortex Clustering and Negative Temperature States in a 2D Bose-Einstein CondensateHayder Salman and Davide Maestrini,


2:40-2:55 The Structure of the Equilibrium Field Distribution in a Discrete Optical Waveguide System with Four-Wave MixingStanislav Derevyanko, Weizmann Institute

of Science, Israel

3:00-3:15 Ground State Solutions of Coupled IR/UV Stationary FilamentsDanhua Wang, University of Vermont,

USA; Alejandro Aceves, Southern Methodist University, USA

3:20-3:35 Dynamics of Bright-Dark Solitons and Their Collisions in the General Multi-Component Yajima-Oikawa SystemSakkaravarthi Karuppaiya and Kanna

Thambithurai, Bishop Heber College, India

3:40-3:55 Pulse Interactions and Bound-State Formation in Non-Local Active-Dissipative EquationsDmitri Tseluiko and Te-Sheng Lin,

Loughborough University, United Kingdom; Marc Pradas, Serafim Kalliadasis, and Demetrios Papageorgiou, Imperial College London, United Kingdom


2:30-2:55 Solute Dynamics Within Settling Marine Snow at Density DiscontinuitiesMorten Iversen, University of Bremen,

Germany

3:00-3:25 Settling and Rising in Density Stratified Fluids: Analysis and ExperimentsRoberto Camassa, University of North

Carolina, Chapel Hill, USA

3:30-3:55 Transcritical Flow of a Stratified Fluid Over Topography and Non-classical Dispersive Shock WavesGennady El, Loughborough University,

United Kingdom


Thursday, August 14

MS91Nonlinear Dispersive Wave Equations4:30 PM-6:30 PMRoom:Recital Room - Music Center

Wave equations take an important place in the literature since they point out important aspects of some physical phenomena which arise, for example, from water wave theory, fiber optics or plasma dynamics. Since linear equations are insufficient to explain nonlinear behaviours like solitary waves, nonlinear wave equations have been proposed to fulfil this need. In this minisymposium, the essential aim is to feature a blend of analytical and numerical studies on various nonlinear dispersive wave equations. The topics include well-posedness, existence of travelling wave solutions, orbital stability of solitary waves and some numerical results.

Organizer: Nilay Duruk MutlubasIstanbul Kemerburgaz University, Turkey

Organizer: Handan BorlukIsik University, Turkey

4:30-4:55 Local Well-posedness for a Class of Nonlocal Evolution Equations of Whitham TypeMats Ehrnstrom, Norwegian University of

Science and Technology, Norway

5:00-5:25 Traveling Surface Waves of Moderate Amplitude in Shallow WaterAnna Geyer and Armengol Gasull,

Universitat Autònoma de Barcelona, Spain

5:30-5:55 Orbital Stability of Solitary Waves of Moderate Amplitude in Shallow WaterNilay Duruk Mutlubas, Istanbul

Kemerburgaz University, Turkey; Anna Geyer, Universitat Autònoma de Barcelona, Spain

6:00-6:25 The Nonlocal Nonlinear Wave Equation with Periodic Boundary Conditions: Analytical and Numerical ResultsHandan Borluk, Isik University, Turkey;

Gulcin M. Muslu, Istanbul Technical University, Turkey

Thursday, August 14

MS90Dynamical Systems and Climate - Part II of II4:30 PM-6:30 PMRoom:Fellows Dining Room - Concourse (1st Floor)

For Part 1 see MS82 Over the past few decades it has become apparent that the Earth’s climate is a rich source of applied mathematical problems, particularly in the fields of dynamical systems and data assimilation. The rigorous study of conceptual models has provided new insight into climate dynamics, along the way necessitating the development of exciting new mathematical tools. This minisymposium will focus on the application of dynamical methods to problems in such diverse areas as data assimilation, desertification, and ocean circulation, with an emphasis on the unique mathematical challenges arising in such studies.

Organizer: Graham CoxUniversity of North Carolina, Chapel Hill, USA

Organizer: Thomas BellskyArizona State University, USA

4:30-4:55 Mixed Mode Oscillations in Conceptual Climate Models: A General PerspectiveEsther Widiasih, University of Hawaii, USA

5:00-5:25 Mixed Mode Oscillations in Conceptual Climate Models: An In-depth DiscussionAndrew Roberts, University of North

Carolina, Chapel Hill, USA; Esther Widiasih, University of Hawaii, USA; Chris Jones, University of North Carolina, Chapel Hill, USA; Martin Wechselberger, University of Sydney, Australia

5:30-5:55 Data Assimilation for Quadratic Dissipative Dynamical SystemsKody Law, King Abdullah University of

Science & Technology (KAUST), Saudi Arabia

6:00-6:25 Automatic Recognition and Tagging of Topologically Different Regimes in Dynamical SystemsJesse Berwald, University of Minnesota,

USA

Thursday, August 14

MS89Nonlinear Waves in Fluid Flows and Their Interaction with Structures - Part II of II4:30 PM-6:30 PMRoom:Jock Colville Hall - Archives Center

For Part 1 see MS81 This session focuses on nonlinear waves in fluid flows and their interaction with structures. Examples include internal and surface waves in the ocean, flexural-gravity waves in floating ice sheets, and hydroelastic waves in industrial or biological fluid systems. Such problems are typically described by nonlinear dispersive PDEs with coupling terms, which require sophisticated analytical techniques and accurate numerical methods to calculate such solutions as solitary waves, breaking waves or waves with a multivalued profile. This session will feature a wide range of talks on the mathematical modeling, numerical simulation and laboratory experiment of such waves.

Organizer: Philippe GuyenneUniversity of Delaware, USA

Organizer: Emilian I. ParauUniversity of East Anglia, United Kingdom

4:30-4:55 On the Interaction Between Surface and Internal WavesWooyoung Choi, New Jersey Institute of

Technology, USA

5:00-5:25 Computing the Pressure in Fully Nonlinear Long-Wave Models for Surface Water WavesHenrik Kalisch, University of Bergen,

Norway

5:30-5:55 Davies Approximation of Levi-Civita’s Surface Condition for Water Waves in the Complex DomainSunao Murashige, Ibaraki University,

Japan; Wooyoung Choi, New Jersey Institute of Technology, USA

6:00-6:25 Axisymmetric Solitary Waves on a Ferrofluid JetMark Blyth, University of East Anglia,

United Kingdom


Thursday, August 14

MS93Discrete and Continuous Nonlocal Wave Equations and Applications - Part III of III4:30 PM-6:00 PMRoom:Bevin Room - Wolfson Hall

For Part 2 see MS85 The session focuses on recent results on nonlinear wave equations with nonlocal terms, including dispersive wave equations coupled with elliptic or parabolic equations. Applications include nonlinear optics in thermal media, water wave models, and coupled nonlinear lattice models. The inclusion of nonlocal terms can produce subtle and physically important effects in the properties of coherent structures, and requires more general analytical and numerical tools. The session will include works motivated by recent experimental studies, as well as more theoretical results on the relevant models.



4:30-4:55 Interaction of Dark Nonlocal SolitonsW. Krolikowski, Australian National

University, Australia

5:00-5:25 Some Results About the Relativistic NLS EquationJuan Pablo Borgna, Universidad

Nacional General Sarmiento, Argentina

5:30-5:55 Optical Solitons in Nematic Liquid Crystals: Continuous and Discrete ModelsPanayotis Panayotaros, IIMAS-

UNAM, Mexico

5:30-5:55 Competitive Geometric Evolution of Network MorphologiesKeith Promislow, Michigan State

University, USA; Shibin Dai, New Mexico State University, USA; Greg Hayrapetyan, Carnegie Mellon University, USA

6:00-6:25 Multiple Water-Vegetation Feedback Loops Lead to Complex Vegetation Diversity Through Competing Turing MechanismsShai Kinast, Yuval R. Zelnik, and Golan

Bel, Ben Gurion University, Israel; Ehud Meron, Ben Gurion University Negev, Israel

Thursday, August 14

MS92Coherent Structures Driven by Coulombic and Other Long Range Interactions - Part II of II4:30 PM-6:30 PMRoom:Club Room - Concourse (1st Floor)

For Part 1 see MS84 Coherent structures (CSs) are fundamental in pattern forming systems, e.g., reaction-diffusion systems, convection, and periodically forced media. Recently, evidences of CSs are also being emerged in systems related to renewable energy devices, e.g., membranes in fuel cells, batteries, and ionic liquids. Such systems extend the reaction-diffusion type systems to incorporate effects like Coulombic interactions and global conservations. The minisymposium goals: (1) to survey the development of models and analysis methods that give rise to CSs and (2) to scrutinize the connections between models and their impacts to real life applications, e.g. renewable energy devices, polymer based media and vegetation.

Organizer: Arik YochelisBen Gurion University Negev, Israel

Organizer: Nir GavishTechnion - Israel Institute of Technology, Israel

4:30-4:55 A Generalized Otha-Kawasaki Model with Asymmetric Long Range InteractionsNir Gavish, Technion - Israel Institute of

Technology, Israel

5:00-5:25 Variational Models and Energy Landscapes Associated with Self-AssemblyRustum Choksi, McGill University, Canada



Thursday, August 14

CP13Mathematical Physics, Materials and Related Problems4:30 PM-6:30 PMRoom:Tizard Room - Concourse (1st Floor)

Chair: Stefan Mancas, Embry-Riddle Aeronautical University, USA

4:30-4:45 Transmission and Reflection of Airy Beams at An Interface of Dielectric MediaRajah P. Varatharajah, North Carolina

A&T State University, USA

4:50-5:05 Ultrashort Pulse Propagation in Periodic Media - Analysis and Novel ApplicationsYonatan Sivan, Ben Gurion University

Negev, Israel

5:10-5:25 Chiral Solitary Waves in Galilean Covariant Fermi Field Theories with Self-InteractionFuad Saradzhev, Athabasca University,

Canada

5:30-5:45 Absolute Stabilization for the Axially Moving Kirchhoff String with Nonlinear Boundary Feedback ControlYuhu Wu and Tielong Shen, Sophia

University, Japan

5:50-6:05 Phase Wave EquationTakashi Odagaki, Tokyo Denki University,

Japan

6:10-6:25 Weierstrass Traveling Wave Solutions for Dissipative EquationsStefan C. Mancas, Embry-Riddle

Aeronautical University, USA

5:30-5:55 Mixing in Stratified Shear Flows: The Central Role of Coherent StructuresColm-cille Caulfield, University of

Cambridge, United Kingdom; Ali Mashayek, Massachusetts Institute of Technology, USA; W. Richard Peltier, University of Toronto, Canada

6:00-6:25 Large Amplitude Solitary Waves and Dispersive Shock Waves in Conduits of Viscous LiquidsMark A. Hoefer and Nicholas K. Lowman,

North Carolina State University, USA; Gennady El, Loughborough University, United Kingdom

Thursday, August 14

MS94Stratified Fluids, Coherent Structures, and Their Interactions - Part II of II4:30 PM-6:30 PMRoom:JCR Games Room – Concourse (Ground Floor)

For Part 1 see MS87 Fluid-structure interactions are ubiquitous in fluid mechanics. The presence of ambient fluid stratification can increase the level of complexity and provide a rich parametric space with new and interesting effects. In this minisymposium, presenters will discuss the dynamics of fluid-structure interactions and multiphase flow in homogeneous and stratified settings. They will explore the resulting fluid flow and emergence of coherent structures in physically relevant problems which pose challenging mathematical questions, including handling varying boundary conditions in the flow. Studies will draw from all aspects of scientific investigations in this area, from experimental, to analytical and numerical results.

Organizer: Shilpa KhatriUniversity of North Carolina, Chapel Hill, USA

Organizer: Roberto CamassaUniversity of North Carolina, Chapel Hill, USA

Organizer: Richard McLaughlinUniversity of North Carolina, Chapel Hill, USA

4:30-4:55 Buoyant Jets and Vortex Rings in StratificationRichard McLaughlin, University of

North Carolina, Chapel Hill, USA

5:00-5:25 On the Extreme Runup of Long Surface Waves on a Vertical BarrierClaudio Viotti, University College

Dublin, Ireland


NW14 Abstracts

Abstracts are printed as submitted.

58 NW14 Abstracts

IP1

Stability and Synchrony in the Kuramoto Model

The phenomenon of the synchronization of weakly coupledoscillators is a old one, first been described by Huygensin his “Horoloquium Oscilatorium.’ Some other exam-ples from science and engineering include the cardiac pace-maker, the instability in the Millenium Bridge, and thesynchronous flashing of fireflies. A canonical model is theKuramoto model

dθidt

= ωi + γ∑j

sin(θj − θi)

We describe the fully synchronized states of this modeltogether with the dimensions of their unstable manifolds.Along the way we will encounter a high dimensional poly-tope, a Coxeter group, and a curious combinatorial iden-tity. This leads to a proof of the existence of a phase tran-sition in the case where the frequencies are chosen from asiid Random variables.

Jared BronskiUniversity of Illinois Urbana-ChampaignDepartment of [email protected]

IP2

Integrability: Initial- Boundary Value Problems in1+1, and Solitons in 3+1

A review will be presented of the two most challengingproblems in the analysis of integrable nonlinear evolutionequations: (a) initial- boundary value problems in 1+1, i.e.evolution equations in one spatial variable, and (b) the con-struction and solution of equations in 3+1. Regarding (a),it will be shown that the so- called unified transform, whichprovides the proper generalization of the inverse scatteringtransform, yields effective formulae for the large t- asymp-totics of a variety of physically significant problems; thisincludes problems on the half-line with t-periodic boundaryconditions. Regarding (b), an integrable generalization ofthe Davey-Stewardson equation 4+2, i.e. four spatial andtwo time variables, will be presented. A reduction of thisequation to an equation in 3+1 will also be discussed. Fur-thermore, one and two soliton solutions for both the 4+2and 3+1 Davey-Stewardson equations will be presented.

Thanasis FokasDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of Cambridge, [email protected]

IP3

Minimal Models for Precipitating Convection

Despite the importance of organized convection (e.g. squalllines and hurricanes), numerical simulations remain a chal-lenge. Comprehensive cloud resolving models would in-clude water vapor, liquid water and ice, and liquid wa-ter would be separated into cloud water and rain water.Here we take a minimalist approach to cloud microphysicsby incorporating fast auto-conversion from cloud to rainwater, and fast condensation and evaporation. Numeri-cal and analytical results will be discussed, e.g., saturatedregions have a linear stability boundary associated withparcel (finite-amplitude) stability in unsaturated regions.

Leslie Smith

Mathematics and Engineering PhysicsUniversity of Wisconsin, [email protected]

IP4

Coherent Structures in 2D Turbulence: Identifica-tion and their Use

Ideas from dynamical systems have recently provided freshinsight into transitional fluid flows. Viewing such flows asa trajectory through a phase space littered with coherentstructures (meaning ’exact’ solutions here) and their sta-ble and unstable manifolds has proved a fruitful way ofunderstanding such flows. Motivated by the challenge ofextending this success to turbulent flows, I will discuss howcoherent structures can be extracted directly from long-time simulations of body-forced turbulence on a 2D torus.These will then be used to ’postdict’ certain statistics ofthe turbulence.

Rich KerswellDepartment of MathematicsUniversity of Bristol, [email protected]

IP5

A Neural Field Model of Binocular Rivalry Waves

Binocular rivalry is the phenomenon where perceptionswitches back and forth between different images presentedto the two eyes. The resulting fluctuations in perceptualdominance and suppression provide a basis for non-invasivestudies of the human visual system and the identificationof possible neural mechanisms underlying conscious visualawareness. In this talk we present a neural field model ofbinocular rivalry waves in visual cortex continuum neuralfields are integro-differential equations that describe thelarge-scale spatiotemporal dynamics of neuronal popula-tions. We derive an analytical expression for the speed ofa binocular rivalry wave as a function of various neurophys-iological parameters, and show how properties of the waveare consistent with the wave-like propagation of perceptualdominance observed in recent psychophysical experiments.We then analyze the effects of extrinsic noise on wave prop-agation in a stochastic version of the neural field model. Weend by describing recent work on rotating rivalry stimuliand direction selectivity.

Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]

IP6

Engineering Extreme Materials with Defects andNonlinearity

We study the fundamental dynamic response of discretenonlinear systems and study the effects of defects in theenergy localization and propagation. We exploit this un-derstanding to create experimentally novel materials anddevices at different scales (for example, for application inenergy absorption, acoustic imaging and energy harvest-ing). We use granular systems as a basic platform for test-ing, and control the constitutive behavior of the new ma-terials selecting the particles geometry, their arrangementand materials properties. Ordered arrangements of par-ticles exhibit a highly nonlinear dynamic response, which

NW14 Abstracts 59

has opened the door to exciting fundamental physical ob-servations (i.e., compact solitary waves, energy trappingphenomena, and acoustic rectification). This talk will fo-cus on energy localization and redirection in one- and two-dimensional systems.

Chiara DaraioETH Zurich, Switzerland and California Institute of [email protected]

IP7

Momentum Maps, Shape Analysis and Solitons

Much of this talk is based on work done with Jerry Mars-den (1942 - 2010) on shared geometric properties in theanalysis of fluid flow and shape transformations. The talkwill discuss uses of geometric mechanics in the problem ofregistration of images, primarily in the example of planarclosed curves. Many types of mathematics apply in thisproblem, including soliton theory and momentum maps.Some trade secrets will be revealed.

Darryl D. HolmImperial College [email protected]

IP8

Symmetry, Modulation and Nonlinear Waves

Modulation underpins many facets of the analysis of non-linear waves and patterns. A new perspective on modula-tion combined with symmetry and conservation laws willbe presented, which leads to a mechanism for the emer-gence of model wave PDEs such as KdV, KP, Boussinesqand others. This combination results in simple geomet-ric formulae for the coefficients. Generalizations to multi-phase wavetrains, systems of conservation laws, Whithamequations with dispersion, and a mechanism for the forma-tion of multi-pulse planforms in pattern formation will alsobe presented.

Tom J. BridgesUniversity of [email protected]

SP1

Martin D. Kruskal Prize Lecture - NonlinearWavesfrom Beaches to Photonics

Based on work of Kruskal et al the Korteweg-deVries equa-tion was found to have many remarkable properties. Theseproperties are shared by many other equations includingthe 2D Kadomtsev-Petvishvili (KP) equation, which arisesin the study of shallow water waves. Some solutions of KPand their relation to waves on shallow beaches will be dis-cussed. Nonlinear waves in photonic periodic lattices willalso be described; photonic graphene is a remarkable case.Since this is an evening lecture, equations and details willbe kept to a minimum, and the lecture will be colloquiumstyle.

Mark AblowitzDept. of Applied MathematicsUniversity of Colorado

[email protected]

CP1

The Rogue Wave Solutions of the Kpi

Rogue wave solutions of integrable partial differential equa-tions are one kind of large-amplitude doubly localized ratio-nal solutions. Recently, the first-order rogue wave solutionof the NLS has been observed in water tanks and opticalfibers. In this talk, we shall provide new rogue wave so-lutions of a well-known (2+1)- dimensional equation: theKPI, from the solutions two (1+1)-dimensional equations:NLS and complex mKdV. The main technique is the Dar-boux transformation.

Jingsong HeNingbo [email protected]

CP1

Mcc Type Strongly Nonlinear Internal Wave Mod-els

We discuss MCC type strongly nonlinear internal longwave models in two- and three-layer fluid systems in de-tail. Their dispersion relations and stability propertiescomparing to coupled Euler equations will be presented.In addition, generalized strongly nonlinear models are alsoconsidered. Non-stationary time evolution for their perfor-mance tests will be presented as well.

Tae-Chang JoInha [email protected]

CP1

Laboratory Experiments and Simulations for Soli-tary Internal Waves with Trapped Cores

Under appropriate conditions, solitary internal waves inthe ocean and atmosphere can develop recirculating re-gions, known as “trapped cores’. Fundamental properties,essential for constructing and testing theoretical models,remain to be quantified experimentally. These include corecirculation and density, as well as mass and energy trans-port, and Richardson number. By using a new technique,we measure these properties in detail. To examine largerwaves, we perform simulations. The corresponding theoryagrees closely with our experiments.

Paolo Luzzatto-FegizUniversity of [email protected]

Karl HelfrichWoods Hole Oceanographic [email protected]

CP1

Internal Waves Incident Upon An Interface

Recent results have shown that a vertical packet of inter-nal waves that are horizontally periodic will develop a dis-continuous mean flow at an interface. Here we considera similar configuration where the waves are not horizon-tally periodic, but instead exist within a wave packet thatis limited both horizontally and vertically. The basic statehas constant stability N in two layers without a shear flow.

60 NW14 Abstracts

The horizontal limit of the wavepacket results in a muchdifferent wave-induced mean flow than the periodic case,as the mean flow is confined to the wavepacket and there-fore must have a zero net flow across any vertical surface.The net effect is that gradients of the mean flow at theinterface are stronger than the periodic case. Waves aretreated with the nonlinear Schrodinger equations that aresolved numerically.

John P. MchughUniversity of New [email protected]

CP1

Nonlinear Harmonic Generation by Internal WaveRefraction

Weakly nonlinear analysis is used to show how internalwave refraction through variable stratification generatesharmonics. Refraction into a strongly stratified pycnoclinelayer will be analyzed, as ocurs for oceanic internal tidesand topographically-generated beams. For large incidenceangles, the lowest harmonic is trapped, and its wavenum-ber selected by a resonance with the natural modes of thepycnocline. Analytic methods are used to calculate thisresonance condition, and the results compared to simula-tion and experiment.

Scott E. WunschJohns Hopkins [email protected]

CP1

Cylindrical Korteweg-De Vries Type Equation forInternal and Surface Ring Waves on a Shear Flow

We study the ring waves in a stratified fluid over a pre-scribed shear flow. A weakly-nonlinear 2+1-dimensionallong wave model is derived from the full set of Euler equa-tions with background stratification and shear flow, writtenin cylindrical coordinates, subject to the boundary condi-tions typical for the oceanographic applications. In theabsence of the shear flow and stratification, the derivedequation reduces to the cylindrical Korteweg -de Vries typeequations obtained by V.D. Lipovskii and R.S. Johnson.The features of the ring waves are then studied numeri-cally using a finite-difference code for the derived model.

Xizheng Zhang, Karima KhusnutdinovaLoughborough University, [email protected], [email protected]

CP2

Model Order Reduction for Coupled NonlinearSchr?dinger Equation

Proper orthogonal decomposition (POD) method is usedto get numerical solution for coupled nonlinear Schrdinger(CNLS) equation in Hamiltonian form. The CNLS equa-tion is discretized in space by finite differences and is solvedin time by midpoint method. Numerical results for CNLSequation with different parameters indicate that the low-dimensional approximations obtained by POD is effectiveand reproduce very well the characteristic dynamics of thesystem, such as preservation of energy and phase spacestructure of the CNLS equation.

Canan Akkoyunlu

Istanbul Kultur UniversityDepartment of Mathematics and Computer [email protected]

Murat UzuncaDepartment of Mathematics & Institute of AppliedMathematicsMiddle East Technical University, [email protected]

Bulent KarasozenMiddle East Technical UniversityInstitute of Applied [email protected]

CP2

Boundary Value Problems for MultidimensionalIntegrable Nonlinear Pdes

The Fokas method, or Unified Transform method, is a sig-nificant novel generalization of the classical inverse scat-tering method, rendering it applicable to initial-boundaryvalue problems (IBVPs) for integrable nonlinear PDEs. Wepresent the implementation of the Fokas method to certainIBVPs for multidimensional integrable nonlinear PDEs. Inparticular, we study the Davey-Stewartson equation (i) onthe half-plane in the case of a time-periodic boundary con-dition, (ii) on the quarter-plane, and (iii) on bounded do-mains.

Iasonas HitzazisDepartment of MathematicsUniverity of Patras, [email protected]

CP2

Variable Separation Solutions and InteractingWaves of a Coupled System of the Modified KdVand Potential Blmp Equations

The multilinear variable separation approach (MLVSA) isapplied to a coupled modified Korteweg de-Vries and po-tential Boiti-Leon-Manna-Pempinelli equations, as a result,the potential fields uy and vy are exactly the universalquantity applicable to all multilinear variable separablesystems. The generalized MLVSA is also applied, and itis found uy (vy) is rightly the subtraction (addition) oftwo universal quantities with different parameters. Theninteractions between periodic waves are discussed, for in-stance, the elastic interaction between two semi-periodicwaves and non-elastic interaction between two periodic in-stantons. An attractive phenomenon is observed that adomion moves along a semi-periodic wave.

Xiaoyan TangEast China Normal [email protected]

Ji LinZhejiang Normal [email protected]

Zufeng LiangHangzou Normal University

NW14 Abstracts 61

[email protected]

CP2

Explicit Construction of the Direct ScatteringTransform for the Benjamin-Ono Equation withRational Initial Conditions

We propose a construction for the scattering data of theBenjamin-Ono equation with a rational initial condition,under mild restrictions. The construction procedure con-sists in building the Jost function solutions explicitly anduse their analyticity properties to recover the reflection co-efficient, eigenvalues, and phase constants. We finish byshowing that this procedure validates certain well-knownformal results obtained in the zero-dispersion limit by Y.Matsuno.

Alfredo N. Wetzel, Peter D. MillerUniversity of Michigan, Ann [email protected], [email protected]

CP3

Solitary Wave Perturbation Theory for Hamilto-nian Systems

Solitary waves in Hamiltonian systems can be parame-terized by conserved quantities and parameters associatedwith the system’s symmetries. When such systems are per-turbed, it is natural to consider slow dynamics constrainedto the solitary wave solution manifold. A standard wayto derive the modulation equations involves direct calcula-tions of the perturbed conserved quantities. However, theevolution of the symmetry parameters containing higherorder, but often important, information is not as readilyobtained. In this talk, singular perturbation theory is em-ployed to obtain the solitary wave modulation equationsfor a general class of Hamiltonian systems. This method-ology is applied to a six-parameter solitary wave solutionfor the (2+1)D Landau-Lifshitz equation that models themagnetization of a thin, ferromagnetic material. Resultsare provided for recent experimental observations of soli-tary waves in a magnetic layer where both damping andlocalized forcing are present.

Lake Bookman, Mark A. HoeferNorth Carolina State [email protected], [email protected]

CP3

Resonance, Small Divisors and the Convergence ofNewton’s Iteration to Solitons

Resonances create the small divisor problem forStokes/Poincare-Lindstedt series. We show throughthe Fifth-Orde KdV equation how the same cause makesNewton’s iteration stall at small residuals, and how to fixthis to converge to a soliton or periodic traveling wave.

John P. BoydUniversity of MichiganAnn Arbor, MI 48109-2143 [email protected]

CP3

Orbital Stability of Solitary Shallow Water Wavesof Moderate Amplitude

We study the orbital stability of solitary traveling wave

solutions of an equation for surface water waves of moder-ate amplitude in the shallow water regime. Our approachis based on a method proposed by Grillakis, Shatah andStrauss in 1987, and relies on a reformulation of the evo-lution equation in Hamiltonian form. We deduce stabilityof solitary waves by proving the convexity of a scalar func-tion, which is based on two nonlinear functionals that arepreserved under the flow.

Anna GeyerUniversity Autonoma de [email protected]

Nilay Duruk MutlubasKemerburgaz University, Istanbul, [email protected]

CP3

Velocity Field in Parametrically Excited SolitaryWaves

Parametrically excited solitary waves are localized struc-tures in high-aspect-ratio free surfaces subject to verticalvibrations. In this talk, we present the first experimentalcharacterization of the hydrodynamics of these waves us-ing Particle Image Velocimetry. Our results confirm theaccuracy of Hamiltonian models with added dissipation indescribing these structures. Our measurements also un-cover the onset of a streaming velocity field which is shownto be as important as other nonlinear terms in the currenttheory.

Leonardo GordilloLaboratoire Matiere et Systemes Complexes (MSC)Universite Paris 7 [email protected]

Nicolas MujicaDepartamento de Fisica, FCFMUniversidad de [email protected]

CP3

Solitary Waves and an N-particle Algorithm for aClass of Euler-Poincare Equations

Nonlinearity arises generically in mathematical models ofphysical phenomena, and the interplay between nonlinear-ity and dispersion is thought to be responsible for manyof these phenomena, such as the existence of travelingwaves. We explore the relation between nonlinearity anddispersion by studying the N-particle system of the Euler-Poincare differential equations, or the EPDiff equations.In particular, we illustrate the existence and dynamics oftraveling wave solutions of the EPDiff equations. Solitarywaves for this class of equations can be made to correspondto interacting particles of a finite-degree-of-freedom Hamil-tonian system. We analyze the dynamics of two-solitarywave interaction and show that two solitons can either scat-ter or capture each other. The scattering or capture orbitsdepend on the singularity level of the solitons, while singu-larity of a soliton is determined by the power of the linearelliptic operator associated with the EPDiff equations.

Long LeeDepartment of MathematicsUniversity of [email protected]

62 NW14 Abstracts

Roberto CamassaUniversity of North [email protected]

Dongyang KuangUniversity of [email protected]

CP3

The (1+2)-Dimensional Sine-Gordon Equation:Soliton Solutions and Spatially Extended Relativis-tic Particles

The (non-integrable) (1+2)-dimensional Sine-Gordonequation does have N-soliton solutions for all N = 1. Multi-soliton solutions propagate rigidly at constant velocitiesthat are higher than or lower than the speed of light. A firstintegral of the equation vanishes on single-soliton solutionsand maps multi-soliton solutions onto structures that arelocalized around soliton junctions. The slower-than-lightstructures emulate spatially extended relativistic particles,whose mass density obeys a source-driven wave equation.

Yair ZarmiBen Gurion University of the [email protected]

CP4

Spectral Band Gaps and Lattice Solitons for theFourth Order Dispersive Nonlinear SchrodingerEquation with Time Periodic Potential

Localization and dynamics of the one-dimensional bihar-monic nonlinear Schrodinger equation in the presence ofan external periodic potential is studied. The band gapstructure is determined using the Floquet-Bloch theoryand the shape of its dispersion/diffraction curves as a func-tion of the fourth order dispersion/diffraction coupling con-stant β is discussed. Contrary to the classical nonlinearSchrodinger equation (with an external periodic potential)here it is found that for a fixed negative value of β, thereexists a nonzero threshold value of potential strength belowwhich there is no first band gap. For increasing values ofpotential amplitudes, the dispersion bands reorient them-selves leading to different soliton forms. Lattice solitonscorresponding to spectral eigenvalues lying the the semi-infinite and first band gap are constructed. Stability prop-erties of various localized lattice modes are analyzed andcontrasted against direct numerical simulations.

Justin ColeFlorida State [email protected]

Ziad MusslimaniDept. of MathematicsFlorida State [email protected]

CP4

Transverse Instability of a Soliton Solution toQuadratic Nonlinear Schrodinger Equation

Madelungs fluid picture is applied to the quadratic nonlin-ear Schrodinger equation. This gives the travelling waveequation that describes ion acoustic wave in plasma withnon-isothermal electrons. The variational method is ap-plied to determine the growth rate of instabilities of a soli-

ton which is perturbed perpendicular to its direction ofpropagation. This gives us the Lagrangian density of thecoupled differential equations. The growth rate can be ob-tained by maximizing the Lagrangian density. By usingthe spectral methods, the unstable planed soliton will beshown a transformation to two-dimensional soliton-like so-lution.

Sarun PhibanchonFaculty of Art and Science, Burapha UniversityChanthaburi, [email protected]

Michael AllenPhysics Department, Mahidol UniversityRama 6 Road, Bangkok, 10400, [email protected]

CP4

On Rational Solutions to Multicomponent Nonlin-ear Derivative Schrodinger Equation

We consider multicomponent derivative nonlinearSchrodinger equations (DNLS) related to Hermitiansymmetric spaces. DNLS were firstly proposed by A.Fordy as generalizations of Kaup-Newell’s equation. Wepresent rational type solutions to DNLS. To do this wemake use of Zakharov-Shabat’s dressing technique adaptedfor quadratic bundles.

Tihomir I. ValchevSchool of Mathematical Sciences,Dublin Institute of [email protected]

CP4

Long-Time Asymptotics for the Defocusing Inte-grable Discrete Nonlinear Schrodinger Equation

We investigate the long-time asymptotics for the defo-cusing integrable discrete nonlinear Schrodinger equationidRn/dt+(Rn+1−2Rn+Rn−1)−|Rn|2(Rn+1+Rn−1) = 0introduced by Ablowitz-Ladik. We employ the inverse scat-tering transform and the Deift-Zhou nonlinear steepest de-scent method. The leading part is a sum of two oscillatoryterms with decay of order t−1/2. Details will appear inJournal of the Mathematical Society of Japan.

Hideshi YamaneKwansei Gakuin [email protected]

CP5

Pipes and Neurons

We exploit a surprising analogy between the subcriticaltransition to turbulence and the dynamics action poten-tials in order to understand the onset of turbulence in pipeflow. The focus here is the transition from localized toexpanding turbulence. Analysis of fronts connecting lami-nar flow (quiescent state) to turbulent flow (excited state)gives the speeds of turbulent-laminar fronts. Combiningwith experiments and simulations we explain the variousstages in the transition to turbulence.

Dwight BarkleyUniversity of WarwickMathematics Institute

NW14 Abstracts 63

[email protected]

Baofang Song, Mukund VasudevanInstitute of Science and Technology [email protected], [email protected]

Marc AvilaUniversity of [email protected]

Bjoern HofInstitute of Science and Technology [email protected]

CP5

Optimal Control in a Mathematical Model of LowGrade Glioma

We address this research to a mathematical model for low-grade glioma treated with chemotherapy. We analyze thedynamics of the model and study the stability of the so-lutions. Besides, we characterize the optimal controls re-lated to drug therapy, using different strategies, includinga quadratic control and a linear control. We establish theexistence of the optimal control, and solve for the controlin both the quadratic and linear case. Finally, from nu-merical simulations, we discuss the optimal strategies fromthe clinical point of view

Juan Belmonte-BeitiaDepartamento de MatematicasUniversidad de Castilla-La [email protected]

CP5

Localized Structures and Their Dynamics in Bio-convection of Euglena Gracilis

We experimentally study localized patterns of suspensionof a phototactic microorganism, Euglena gracilis, illumi-nated from the bottom. By using annular container, twobasic types of localized patterns were isolated. They aresimilar to those observed in thermal convection of binaryfluid mixtures, although the governing equations for thissystem is not known. We will also report their dynamicsand statistical analysis related to the bistability and pho-totactic responses of the microorganism.

Makoto Iima, Erika Shoji, Akinori Awazu, HirakuNishimori, Shunsuke IzumiHiroshima [email protected], [email protected], [email protected], [email protected], [email protected]

CP5

Models for Adaptive Feeding and Plankton Popu-lations

In this presentation, we develop (1) a piecewise-smoothdynamical system and (2) reformulate it as a fast-slowdynamical system to account for prey preference, flexi-ble feeding behaviour or rapid evolution, and an ecologi-cal trade-off (all of which have been observed in plankton).We discuss connections between Filippov and fast-slow sys-tems, and compare our model predictions with data on

protozoan predator and two different phytoplankton preygroups collected from Lake Constance.

Sofia Piltz, Mason A. PorterUniversity of [email protected], [email protected]

Philip K. MainiOxford University, Mathematical Inst. 24-29 St. GilesOxford. OX1 [email protected]

CP5

Self-Organisation in a Reaction-Diffusion Systemwith a Non-Diffusing Component

Motivated by the regulation mechanism behind position-ing of flagellar basal bodies in bacteria, we study a modelsystem where a diffusion-driven instability leads to pat-tern formation. The model includes three species and itsdynamics is described by a pair of reaction-diffusion equa-tions coupled to an ODE. We study how the presence ofa non-diffusing species impacts the analytical properties ofthe solution and the resulting pattern.

Peter RashkovPhilipps-Universitat [email protected]

CP5

On a Volume-Surface Reaction-Diffusion Sys-tem with Nonlinear Boundary Coupling: Well-Posedness and Exponential Convergence to Equi-librium

We consider a model system consisting of two reaction-diffusion equations, where one specie diffuses in a volumewhile the other specie diffuses on the surface which sur-rounds the volume. The two equations are coupled vianonlinear reversible Robin-type boundary conditions forthe volume specie and a matching reversible source termfor the boundary specie. As a consequence the total massof the species is conserved. The considered system is mo-tivated by models for asymmetric stem cell division. Wefirst prove the existence of a unique weak solution via an it-erative method of converging upper and lower solutions toovercome the difficulties of the nonlinear boundary terms.Secondly, we show explicit exponential convergence to equi-librium via an entropy method after deriving a suitableentropy entropy-dissipation estimate.

Bao Q. TangInstitute of Mathematics and Scientific ComputingUniversity of Graz, [email protected]

Klemens FellnerInstitute for Mathematics and Scientific ComputationUniversity of Graz, [email protected]

Evangelos LatosInstitute of Mathematics and Scientific ComputingUniversity of Graz, [email protected]

CP6

Coherent Structures Inhibition and Destruction in

64 NW14 Abstracts

the Taylor-Couette System

TaylorCouette flow remains one of the most widely stud-ied problems. This is certainly due to the various impact-ing fundamental and applied applications instilled by sucharchetype flow.The Taylor vortices are coherent structuresknown to be omnipresent whatever is the flow regime. Sup-pression of these coherent structures is searched for sev-eral industrial processes such as crystal growth and os-motic/photonic water purification. A control strategy issuggested to obliterate or inhibit the coherent structures ina TaylorCouette flow. It consists in effecting minute radialpulsatile motion of the inner cylinder cross-section. Thesuperimposed modulations combined with the free surfacedynamics suppress both the Ekman and Taylor coherentstructures. When eliminated, fluid particles are no longertrapped within the Ekman or Taylor vortices. This yieldssignificant increase in the axial and azimuthal velocity fluc-tuations, which results in enhanced flow mixing.

Oualli HamidEMP, [email protected]

Mekadem MahmoudEMP, [email protected]

Bouabdallah AhceneUSTHB, [email protected]

CP6

Large Amplitude Solitary Waves and DispersiveShock Waves in Conduits of Viscous Liquids: Ex-perimental Investigation

The evolution of the interface separating a buoyant con-duit of viscous fluid rising through a more viscous, exteriorfluid is governed, counterintuitively, by the interplay be-tween nonlinearity and dispersion, given sufficiently highviscosity contrast. Here, we present the results of quantita-tive, experimental investigations into large amplitude soli-tary wave interactions and dispersive shock waves (DSWs).Overtaking interactions of large amplitude solitary wavesare shown to exhibit nearly elastic collisions and universalinteraction geometries according to the Lax categories forKdV solitons. Further, we conduct experiments on well-developed DSWs and demonstrate favorable comparisonwith Whitham-El modulation theory. We also report ob-servations of novel interaction experiments. Viscous liquidconduits provide a well-understood, controlled, table-topenvironment in which to study universal properties of dis-persive hydrodynamics.

Mark A. HoeferNorth Carolina State [email protected]

Nicholas K. LowmanDepartment of MathematicsNorth Carolina State [email protected]

CP6

On the Unified Wave Model (uwm) for Smooth andPeaked/cusped Solitary Waves

Based on the symmetry and fully nonlinear wave equations,

a unified wave model (UWM) based on the symmetry andthe fully nonlinear wave equations is put forward for pro-gressive waves with permanent form in finite water depth.The UWM admits not only all smooth waves but also thepeaked/cusped solitary waves. So, the UWM unifies thesmooth and peaked/cusped solitary waves in finite waterdepth, for the first time. Some unusual characteristics ofthe peaked waves are found. For example, unlike smoothwaves, the phase speed of peaked solitary waves has noth-ing to do with the wave height. Besides, it is found thata cusped solitary wave is consist of an infinite number ofpeaked ones: this reveals the close relationship betweenthe peaked and cusped solitary waves. The UWM deep-ens and enriches our understandings about the smooth andpeaked/cusped waves as a whole.

Shijun LiaoShanghai Jiaotong [email protected]

CP6

Large Amplitude Solitary Waves and DispersiveShock Waves in Conduits of Viscous Liquids:Model Derivation and Modulation Theory

The evolution of the interface separating a buoyant con-duit of viscous fluid rising through a more viscous, exteriorfluid is governed, counterintuitively, by the interplay be-tween nonlinearity and dispersion, given sufficiently highviscosity contrast. In this talk, a derivation of the scalarinterfacial equation via an asymptotic, multiple scales pro-cedure is presented. Perturbations about a state of ver-tically uniform pipe flow are considered in the context ofthe coupled fluid equations. The approximate model isshown to be valid for long times and large amplitudes undermodest physical assumptions. We then apply Whitham-Elmodulation theory to derive analytical predictions for keyproperties of dispersive shock wave solutions, as well asdemonstrate novel multiphase behavior which results froma turning point in the dispersion relation. This talk estab-lishes the theoretical background for quantitative experi-ments on solitons and DSWs in this simple, table-top fluidsetting.

Nicholas K. LowmanDepartment of MathematicsNorth Carolina State [email protected]


CP6

Controlling the Position of Traveling Waves inReaction-Diffusion Systems

We present a method to control the position as a func-tion of time of one-dimensional traveling wave solutions toreaction-diffusion systems according to a pre-specified pro-tocol of motion. Given this protocol, the control functionis found as the solution of a perturbatively derived inte-gral equation. We derive an analytical expression for thespace and time dependent control function f (x, t) that isvalid for arbitrary protocols and many reaction-diffusionsystems. These results are close to numerically computedoptimal controls. The control can be expressed in terms ofthe uncontrolled wave profile and its propagation velocity,rendering detailed knowledge of the reaction kinetics un-

NW14 Abstracts 65

necessary. An extension to two higher dimensions allows aprecise control of the shape of patterns of reaction-diffusionsystems.

Jakob Lober, Harald EngelInstitute of Theoretical PhysicsTechnical University [email protected], [email protected]

CP6

Interaction of a Weak Discontinuity Wave with El-ementary Waves of the Riemann Problem for EulerEquations of Gasdynamics

We investigate the effects of initial states and the shockstrength on the jumps in shock acceleration, and the am-plitudes of reflected and transmitted waves. The test-dataare considered for the three Riemann problems to analyzethe situation when the initial discontinuity breaks up intotwo shocks and a characteristic shock. It is noticed thatfor a weak shock, the jump in its acceleration due to an in-teraction with a weak discontinuity wave can be zero onlywhen the incident wave belongs to the same family as theshock.

Vishnu D. SharmaIndian Institute of Tecnology [email protected]

CP7

Oscillons in a Parametrically Forced PDE

Spatially localized, time-periodic structures are commonin pattern-forming systems, appearing in fluid mechanics,chemical reactions, and granular media. We examine theexistence of oscillatory localized states in a PDE modelwith single frequency time dependent forcing, where theprimary pattern appears with non-zero wavenumber.

Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]

Abeer Al-Nahdi, Jitse NiesenUniversity of [email protected], [email protected]

CP7

Hopf Bifurcation from Fronts in the Cahn-HilliardEquation

We study Hopf bifurcation from traveling-front solutionsin the Cahn-Hilliard equation. Models of this form havebeen used to study numerous physical phenomena, includ-ing pattern formation in chemical deposition and precipi-tation processes. Technically we contribute a simple anddirect functional analytic method to study bifurcation inthe presence of essential spectrum. Our approach uses ex-ponential weights to recover Fredholm properties, spectralflow ideas to compute Fredholm indices, and mass conser-vation to account for negative index.

Ryan Goh, Arnd ScheelUniversity of Minnesota

[email protected], [email protected]

CP7

New Exact Solution for Nonlinear Interaction ofTwo Pulsatory Waves of the Korteweg De VriesEquation in An Invariant Zigzag Structure

Interaction of two pulsatory waves of the KdV equationis treated by a novel method of solving nonlinear PDEsby invariant structures, which continues classical meth-ods of undetermined coefficients and separation of vari-ables by developing experimental and theoretical comput-ing. Using this approach a new solution for pulsatorywaves, which includes the two-solitons solution, is devel-oped experimentally and proved theoretically by employ-ing a zigzag, hyperbolic-tangent structure. Convergence,tolerance, and summation of the structural approximationare discussed.

Victor A. MiroshnikovCollege of Mount Saint [email protected]

CP7

Inertial Waves and Pattern Formation Inside a Ro-tating Cylinder Partially Filled with Liquid

We consider a rapidly rotating horizontal cylinder partiallyfilled with granular medium and/or fluid under gravityor vibration. In the rotating frame gravity oscillates andinduces fluid oscillations, which take the form of inertialwaves under resonance conditions. Dependently on the ex-perimental conditions waves with different azimuthal andaxial wavenumbers are excited. The inertial waves gen-erate averaged fluid flows in the direction of propagationand bring to growth of regular patterns on the fluid-sandinterface.

Denis A. Polezhaev, Victor Kozlov, Veronika DyakovaThe laboratory of vibrational hydromechanicsPerm State Humanitarian Pedagogical [email protected], [email protected],[email protected]

CP7

Quasipatterns in Coupled Reaction-Diffusion Prob-lems

The nonlinear interaction between waves of different wave-lengths is a mechanism that can stabilise 12-fold quasi-patterns (two-dimensional patterns that are quasiperiodicin all directions but that have 30◦ rotation symmetry onaverage). Here, we investigate how coupling two pattern-forming Turing systems can lead to these quasipatternsbeing formed.

Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]

CP7

Vibrational Hydrodynamic Top Wave Instabilityand Pattern Formation

Flows excited by light free sphere in cavity with liquidrotating around horizontal axis are experimentally inves-tigated. Sphere commits differential rotation caused by

66 NW14 Abstracts

oscillating external force (vibrational hydrodynamic top).Main flow has shape of 2D column. New instability is foundazimuthal wave at column boundary and two-dimensionalvortex system inside it. Stability threshold is one order ofmagnitude lower compare to differential rotation of spherefixed on axis. Supercritical flows and transition sequencesare studied.

Stanislav SubbotinPerm State Humanitarian Pedagogical [email protected]

Victor KozlovThe laboratory of vibrational hydromechanicsPerm State Humanitarian Pedagogical [email protected]

Nikolay KozlovDepartment of General and Experimental PhysicsPerm State Pedagogical University, Perm, [email protected]

CP8

Complex Mode Dynamics of Coupled Wave Oscil-lators

We show how nonlinear coherent waves localized in a fewwells of a periodic potential can act analogously to a chainof coupled oscillators. We identify the small-amplitude os-cillation modes of this system, demonstrate their extensionto the large amplitude regime and reveal complex behaviorsuch as the breakdown of Josephson-like oscillations, thedestabilization of fundamental oscillation modes and theemergence of chaotic dynamics.

Tristram J. AlexanderUNSW [email protected]

Dong Yan, P. KevrekidisUniversity of [email protected], [email protected]

CP8

Modulation Theory for the Fkdvb Equation Con-structing Periodic Solutions

We present a multiple-scale perturbation technique for ob-taining solutions to the forced Korteweg de Vries-Burgersequation. The first order solution in the perturbation hi-erarchy is the modulated cnoidal wave equation. From thesecond order equation in the hierarchy, we find a system ofodes governing the slow variation of the properties of thecnoidal wave. This is achieved by imposing an extra condi-tion at second order. We then construct periodic solutionsand examine their stability.

Laura HattamMonash [email protected]

CP8

New Criteria Preventing Hamiltonian-Hopf Bifur-cations Using Graphical Krein Signature

Linear stability of equilibria in Hamiltonian systems ischaracterized by a restriction of the spectrum of the lin-earized problem to the imaginary axis. If the Hamilto-

nian is indefinite a stable equilibria under a parameterchange in a system may be subject to instability througha Hamiltonian-Hopf (HH) bifurcation. HH bifurcationsare generic if two purely imaginary eigenvalues of oppositeKrein signature are close to each other. But it is possi-ble that under a particular perturbation eigenvalues passeach other and do not bifurcate; it happens when the per-turbation is definite [Krein & Ljubarski] or if the systemhas an additional symmetry [Melbourne et al.]. Using thegraphical Krein signature we present a new type of mech-anism that prevents HH bifurcations. Although such amechanism is non generic it may commonly appear in ap-plications. Surprisingly the conditions appear to use infor-mation that may not be visible if one considers only thetypical form of the eigenvalue problem.

Richard KollarComenius UniversityDepartment of Applied Mathematics and [email protected]

Peter MillerUniversity of [email protected]

CP8

Persistence Results for Nonlocal Perturbations onUnbounded Domains

The main focus of this talk will be to outline a, quite gen-eral, method to show persistence of coherent structures forsufficiently small non-locality in spatially-extended PDEs.As an example, the existence of stationary solutions fora nonlocal version of the Fisher-Kolmogorov-Petrovsky-Piskounov (FKPP) equation on the unbounded domain R

d

will be considered. It will be shown that only two boundednon-negative stationary solutions of the nonlocal FKPPequation can exist for sufficiently small nonlocality.

Christian Kuehn, Franz AchleitnerVienna University of [email protected], [email protected]

CP8

Pullback Attractor for the Non-AutonomousStochastic Damped Wave Equations on Boundedand Unbounded Domains

This paper is devoted to dierential equations of the dampedwave equations with both non-autonomous deterministicand random forcing terms. On unbounded domain, weshow the sufficient and necessary condition for existenceof pullback attractors for the non-autonomous stochas-tic damped wave equations on unbounded domain by es-tablishing pullback absorbing set and pullback asymptoticcompactness of the cocycle in a certain parameter region,where the uniform estimates on the tails of solutions areemployed to overcome the non-compactness embeddings.On bounded domain, we prove the existence of pullback at-tractors for the non-autonomous stochastic damped waveequations by establishing pullback absorbing set and pull-back condition in a certain parameter region. At the sametime, when the deterministic forcing terms is periodic, weobtain the pullback attractor is also periodic.

Hongyan LiShanghai University of Engineering Science

NW14 Abstracts 67

[email protected]

CP9

Simulating Wall-Mode Convection: NumericalTechniques and First Results

We present simulations of strongly nonlinear wall-modeconvection in a rapidly rotating container. Using theasymptotically reduced model by Vasil et al., we exam-ine the development of the wall-mode instability and sub-sequent pattern formation in isolation from bulk con-vection. This system includes nonlocal and nonlinearbounary conditions, and separate prognostic equations forthe barotropic and baroclinic components of the flow,which we implement using Dedalus, a new open-sourcepseudospectral code.

Keaton BurnsMIT Kavli Institute for Astrophysics and Space [email protected]

Geoffrey M. VasilTheoretical Astrophysics CenterAstronomy Department, University of California,[email protected]

CP9

Time-Averaging and Error Estimates for ReducedFluid Models.

I will discuss the application of time-averaging in gettingrigorous error estimates of some reduced fluid models, in-cluding the quasi-geostrophic approximation, incompress-ible approximation and zonal flows. The spatial boundarycan be present as a non-penetrable solid wall. I will show avery recent (and somewhat surprising) result on the ε2 ac-curacy of incompressible approximation of Euler equations,thanks to several decoupling properties.

Bin Cheng

(SoMSS) School of Mathematical and Statistical SciencesArizona State [email protected]

CP9

Optimal High-Order Diagonally-Implicit Runge-Kutta Schemes for Nonlinear Diffusive Systems onAtmospheric Boundary Layer

Nonlinear diffusion equations are extensively applicable indiverse fields of science and engineering. Numerical stabil-ity is a common concern in this class of equations. In thepresent study, a three-stage third-order diagonally-implicitRunge-Kutta (DIRK) scheme is introduced by optimizingthe error and linear stability analysis for a commonly usednonlinear diffusive system in atmospheric boundary layer.The proposed scheme is stable for a wide range of timesteps and able to resolve different diffusive systems withdiagnostic turbulence closures, or prognostic ones with adiagnostic length scale, with enhanced accuracy and stabil-ity compared to current schemes. It maintains A-stability,which makes it appropriate for the solution of stiff prob-lems. The procedure implemented in this study is quitegeneral and can be used in other diffusive systems as well.

Farshid NazariUniversity of Ottawa

University of [email protected]

Abdolmajid MohammadianUniversity of [email protected]

Martin Charron, Ayrton ZadraEnvironment [email protected], [email protected]

CP9

Interaction of Atmospheric Vortex with A Land

We show that the complex behavior of the tropical cy-clone making landfall can be explained in the frame of twodimensional barotropic model obtained by averaging overthe hight of the primitive system of equations of the at-mosphere dynamics. In particular, this behavior includesa significant track deflection, sudden decay and intensifi-cation. In contrast to other model, where first the addi-tional physically reasonable simplifications are made, wedeal with special classes of solutions to the full system.This allows us not to lose the symmetries of the modeland to catch the complicated features of the full model.Our theoretical considerations are confirmed by numericsmade within a two dimensional barotropic model and are ina good compliance with experimental data. In particular,our method is able to explain the phenomenon of attractionof the cyclone to the land and interaction of the cyclonewith an island.

Olga S. RozanovaMoscow State UniversityMathematics and Mechanics [email protected]

CP9

Atmospheric Moisture Transport: Stochastic Dy-namics of the Advection-Condensation Equation

Transport of atmospheric moisture is studied using astochastic advection-condensation model. Water vapor isadvected by a prescribed velocity field and condensationoccurs as fluid parcels enter regions of low saturation hu-midity. In contrast to previous studies, we focus on twovelocity models with spatial correlation: single-vortex stir-ring and the random sine flow. We predict the total mois-ture decay rate in the initial value problem and investigatethe spatial moisture distribution for the steady-state prob-lem.

Yue-Kin TsangIREAPUniversity of [email protected]

Jacques VannesteSchool of MathematicsUniversity of [email protected]

CP9

On the Asymptotics of Nonlinear Wall-LocalizedThermal Convection Waves

We describe an asymptotically reduced model of multiscalewall-mode convection in a rapidly rotating container. The

68 NW14 Abstracts

bulk-interior dynamics drives small-scale flow within side-wall boundary layers, and the boundary layers feed backonto the interior via a nonlinear and non-local boundaryconditions. These new PDE’s contain the results from pre-vious linear theory but in an elementary fashion and alsoprovide a new avenue for investigating several interestingphenomena in a strongly nonlinear regime.

Geoffrey M. VasilTheoretical Astrophysics CenterAstronomy Department, University of California,[email protected]

Keaton BurnsMIT Kavli Institute for Astrophysics and Space [email protected]

CP10

A Theory of Weakly Non-Linear Detonations

We derive a new weakly non-linear asymptotic model ofdetonation waves that captures the rich dynamics observedin solutions of the reactive Euler equations. We investigatethe traveling wave solutions of the asymptotic model andtheir linear stability. The non-linear dynamics of the modelare investigated by direct numerical simulations. Predic-tions of the asymptotic equations are compared quantita-tively with the full reactive Euler equations.

Luiz [email protected]

Aslan R. KasimovDivision of Mathematical & Computer Sciences andEngineeringKing Abdullah University of Science and [email protected]

Rodolfo R. RosalesMassachusetts Inst of TechDepartment of [email protected]

CP10

Diffraction and Reflection of a Weak Shock at aRight-Angled Wedge in Real Fluids

Shock reflection-diffraction problem is one of the most chal-lenging problems for the mathematical theory of multidi-mensional conservation law. Since at high pressure or lowtemperature, the behavior of gases deviates from the idealgas law and follows the van der Waals gas, we study herethe reflection-diffraction phenomenon of a weak shock ata right-angled wedge for the two-dimensional compressibleEuler system, modeled by the van der Waals equation ofstate. Using asymptotic expansions,some basic features ofthe phenomenon and the nature of flow pattern are ex-plored within the context of a real gas. In this talk, wediscuss how the real gas effects influence the nature of theself-similar flow patterns, relative to what it would havebeen in the ideal gas case.

Neelam GuptaIndian Institute of technology Bombay

[email protected]

CP10

Pattern Formation in a Circular Hydraulic Jump

When a vertical jet of viscous fluid strikes a horizontalplate, a circular hydraulic jump occurs at some distancefrom the jet impact point. Under certain conditions, thecircular symmetry of the jump can break to give rise to sta-tionary or rotating polygonal patterns. The talk describesexperimental observations of the symmetry breaking and amodel for the polygonal pattern formation.

Aslan R. KasimovDivision of Mathematical & Computer Sciences andEngineeringKing Abdullah University of Science and [email protected]

CP10

Nonlinear Energy Transfer Between Fluid Sloshingand Vessel Motion

This talk identifies a mechanism leading to an energy ex-change between a sloshing fluid and the vessel containingthe fluid. The theory is developed for Cooker’s penduloussloshing experiment where a rectangular vessel is partiallyfilled with fluid and suspended by two cables. Close to aninternal 1 : 1 resonance, the energy transfer is manifestedby a heteroclinic connection which connects the purelysymmetric sloshing modes to the purely anti-symmetricsloshing modes leading to slosh-induced destabilization.

Matthew R. TurnerUniversity of [email protected]

Tom J. Bridges, Hamid Alemi ArdakaniUniversity of [email protected], [email protected]

CP10

Fluid Ratcheting by Oscillating Channel Walls withSawteeth

Motions rectified by symmetry-breaking mechanisms in os-cillating flows have been of great interest in biological lo-comotion and engineering applications. Inspired by an ex-periment that demonstrates that fluid can be pumped fromone end to the other in a narrow channel using the vibra-tional motions of the sawtooth channel walls, we put for-ward here a theory describing the ratcheting effect of fluid.In a conformally transformed plane, the Stokes boundarylayer flow is analysed, revealing the nonlinear effects driv-ing the rectified flow and its complex spatial structure.Whereas the wall sawtooth shape is a source of asymmetry,the difference in entrance and exit flow conditions due tothe geometries at the channel ends is found to be a secondsource to break the left-right symmetry of the system.

Jie YuNorth Carolina State Universityjie [email protected]

CP11

Ocean Wave Energy Potential and Microseisms

Ocean gravity waves driven by wind and atmospheric pres-

NW14 Abstracts 69

sure can generate pressure variations on the sea floor thatare at the origin of microseisms. We will be concerned withsecondary microseisms with a frequency twice that of thecausative wave and amplitude independent of the depth.We need to know the sea states that allow pressure varia-tions large enough to generate microseisms and we need tounderstand how pressure variations vary in space and timeand how they are linked to the sea floor. We will showthe conditions on different parameters to obtain pressurevariation able to generate microseisms and we will studythe pressure with respect to different parameters in orderto illustrate our theoretical results.

Paul ChristodoulidesCyprus University of TechnologyFaculty of Engineering and [email protected]

Lauranne PelletEcole Centrale [email protected]

Frederic DiasUniversity College DublinEcole Normale Superieure de [email protected]

CP11

On Periodic Solutions of a Model Equation for Sur-face Waves of Moderate Amplitude in Shallow Wa-ter

The work which will be presented is mainly on a nonlinearevolution equation for surface waves of moderate amplitudein shallow water given below:

ut + ux +3

2εuux − 3

8ε2u2ux +

3

16ε3u3ux (1)

+μ

12(uxxx − uxxt) +

7ε

24μ(uuxxx + 2uxuxx) = 0, x ∈ R, t > 0.

Here u(x, t) is the free surface elevation and ε and μ rep-resent the amplitude and shallowness parameters, respec-tively. Solutions of the Cauchy problem corresponding to(1) which are spatially periodic of period 1 are investi-gated. Local well-posedness is attained by an approachdue to Kato which is based on semigroup theory for quasi-linear equations. Moreover, it is shown that singularitiesfor the model equation can occur only in the form of wavebreaking.

Nilay Duruk MutlubasIstanbul Kemerburgaz [email protected]

CP11

Solitary Waves Without Dispersive Terms: theShallow Water Equations over a Periodic Bottom

The shallow water equations are a non-dispersive hyper-bolic system and their solutions typically involve shockwaves. We show by computational experiment that in thepresence of periodic bathymetry, solutions may be charac-terized instead by solitary wave formation. Unlike solitarywave solutions of the KdV or Boussinesq equations, thesewaves arise in the absence of any dispersive terms. In-stead, they result from effective dispersion caused by wavediffraction and reflection.

David I. Ketcheson

Mathematical and Computer Sciences & EngineeringKing Abdullah University of Science & [email protected]

Manuel Quezada De LunaTexas A&M [email protected]

CP11

Interaction of Strongly Nonlinear Waves on theFree Surface of Non-Conducting Fluid under theAction of Horizontal Electric Field

In the present work we consider the problem of free sur-face motion of the fluid with high dielectric constant in thestrong horizontal electric field. It is shown that nonlinearsurface waves can propagate nondispersively in the direc-tion of electric field . Moreover, the counter-propagatingsolitary weakly nonlinear waves preserve the initial formafter collision. The question arises as to whether the sametendency is observed for strongly nonlinear waves. We haveshown that collisions of strongly nonlinear waves are elas-tic, i.e., the energy of solitary wave does not change. How-ever, results of our numerical simulations indicate that, ingeneral case, the interaction of strongly nonlinear wavesleads to the shape distortion and formation of regions withhigh surface steepness.

Evgeny KochurinInstitute of Electrophysics, Ural Division of [email protected]

Nikolay ZubarevInstitute of Electrophysics, Ural Division of RAS,P. N. Lebedev Physical Institute, [email protected]

CP11

High Order Hamiltonian Water Wave Models withWave-Breaking Mechanism

Based on the Hamiltonian formulation of water waves, wederive higher order Hamiltonian equations by Taylor ex-pansions of the potential and the vertical velocity aroundthe still water level. The polynomial expansion in waveheight is mixed with pseudo-differential operators that pre-serve the exact dispersion relation. The consistent approx-imate equations have inherited the Hamiltonian structureand give exact conservation of the approximate energy. Inorder to deal with breaking waves, we designed an eddyviscosity model that is applicable for fully dispersive equa-tions. As breaking trigger mechanism we use a kinematiccriterion based on the quotient of horizontal fluid veloc-ity at the crest and the crest speed. The performanceis illustrated by comparing simulations with experimentaldata obtained at hydrodynamic laboratory. The compari-son shows that the higher order models perform quite well;the extension with the breaking wave mechanism improvesthe simulations.

Ruddy KurniaApplied Mathematics, University of [email protected]

E. Van GroesenUniversity of TwenteLabMath-Indonesia

70 NW14 Abstracts

[email protected]

CP11

The Higher-Order Boussinesq Equation with Peri-odic Boundary Conditions: Analytical and Numer-ical Results

We consider the higher-order Boussinesq (HBQ) equationproposed in [P. Rosenau, ”Dynamics of dense discrete sys-tems”, Prog. Theor. Phys. 79, 1028-1042, (1988)], [G.Schneider, C. E. Wayne, ”Kawahara dynamics in dispersivemedia”, Physica D 152-153, 384-394, (2001)], [N. Duruk,A. Erkip, H. A. Erbay, ”A higher-order Boussinesq equa-tion in locally non-linear theory of one-dimensional non-local elasticity”, IMA Journal of Applied Mathematics 74,97-106, (2009)]. We propose a Fourier pseudo-spectral nu-merical method for the HBQ equation. We then prove theconvergence of numerical scheme in the energy space. Weconsider three test problems concerning the propagationof a single solitary wave, the interaction of two solitarywaves and a solution that blows up in finite time. Thenumerical results show that the Fourier pseudo-spectralmethod provides highly accurate results. This work hasbeen supported by the Scientific and Technological Re-search Council of Turkey (TUBITAK) under the projectMFAG-113F114.

Goksu Topkarci, Gulcin M. MusluDepartment of Mathematics, Istanbul [email protected], [email protected]

Handan BorlukDepartment of Mathematics, Isik [email protected]

CP12

A Multiscale Continuation Algorithm for BinaryRydberg-Dressed Bose-Einstein Condensates

We study a multiscale continuation algorithm for bi-nary Rydberg-dressed Bose-Einstein condensates which isgoverned by a system of the Gross-Pitaevskii equations(GPEs). The proposed four-parameter continuation al-gorithm has the advantage that we can obtain the con-tours of the wave functions ψ1 and ψ2 for various valuesof μ11 = μ22 ∈ [0, μ∗

1] and μ12 ∈ [0, μ∗2], where we only

need to trace the ground state solution curve once. Ournumerical experiments show that the proposed algorithmoutperforms the classical continuation algorithm, and isvery competitive compared to other numerical methods.

Cheng-Sheng ChienChing Yin UniversityJungli, [email protected]

Sirilak SriburadetNational Chung Hsing [email protected]

Yun-Shih WangChien Hsin University of Science and Technology, [email protected]

CP12

The Structure of the Equilibrium Field Distribu-tion in a Discrete Optical Waveguide System with

Four-Wave Mixing

Statistical mechanics of two coupled vector fields is stud-ied within the framework of the tight-binding model thatdescribes propagation of polarized light in discrete waveg-uides in the presence of the four-wave mixing. The equi-librium properties of the polarization state are describedin terms of the Gibbs measure with positive temperature.The transition line T = ∞ is established beyond whichthe discrete vector solitons are created. In the limit of thelarge nonlinearity an analytical expression for the distribu-tion of Stokes parameters is obtained which is found to bedependent only on the statistical properties of the initialpolarization state and not on the strength of the nonlin-earity. The evolution of the system to the final equilibriumstate is shown to pass through the intermediate stage whenthe energy exchange between the waveveguides is still neg-ligible.

Stanislav DerevyankoWeizmann Institute of [email protected]

CP12

Dynamics of Bright-Dark Solitons and Their Col-lisions in the General Multi-Component Yajima-Oikawa System

We consider a general multi-component Yajima-Oikawasystem governing the dynamics of nonlinear resonance in-teraction of multiple short waves with a long wave in one di-mension. We construct the exact bright-dark (mixed) soli-ton solution by using the Hirota’s bilinearization method.By performing an asymptotic analysis, we unravel twotypes of fascinating energy sharing collisions and also thestandard elastic collision of bright-dark solitons. The dy-namics of soliton bound states is also explored.

Sakkaravarthi KaruppaiyaBishop Heber [email protected]

Kanna ThambithuraiBishop Heber College, Tiruchirappalli–620 017kanna [email protected]

CP12

Vortex Clustering and Negative TemperatureStates in a 2D Bose-Einstein Condensate

In this work we investigate the question of clustering oflike signed vortices in a two-dimensional Bose-Einstein con-densate. Such clustering can be understood in terms ofnegative temperature states of a vortex gas. Due to thelong-range nature of the Coloumb-like interactions in pointvortex flows, these negative temperature states strongly de-pend on the shape of the geometry in which this clusteringphenomena is considered. We analyze the problem of clus-tering of point vortices in a number of different regions.We present a theory to uncover the regimes for which clus-tering of like signed vortices can occur and compare ourpredictions with numerical simulations of a point vortexgas. We also extend our results to the Gross-Pitaevskiimodel of a Bose gas by performing numerical simulationsfor a range of vortex configurations using parameters thatare relevant to current experiments.

Hayder Salman, Davide MaestriniUniversity of East Anglia

NW14 Abstracts 71


CP12

Pulse Interactions and Bound-State Formation inNon-Local Active-Dissipative Equations

We analyse coherent structures in active-dissipative equa-tions that in addition contain non-local contributions in theform of pseudo-differential operators. Such equations arisee.g. in the modelling of a liquid film flow in the presenceof various external effects. We develop a weak-interactiontheory of pulses in such equations and demonstrate thatpulse interactions and bound-state formation are stronglyinfluenced by non-locality and are characterised by severalfeatures that are not present in local equations.

Dmitri TseluikoDepartment of Mathematical [email protected]

Te-Sheng LinDepartment of Mathematical SciencesLoughborough [email protected]

Marc PradasDepartment of Mathematical [email protected]

Serafim KalliadasisDepartment of Chemical EngineeringImperial College [email protected]

Demetrios PapageorgiouDepartment of MathematicsImperial College London, [email protected]

CP12

Ground State Solutions of Coupled IR/UV Station-ary Filaments

The ground state solutions of coupled infrared (IR) / ul-traviolet (UV) stationary filaments have been studied bothanalytically and numerically. The UV pulse have exactTownes solition power for the small IR pulse. And theeigenstates of the UV Townes branch where the IR fila-ment is no longer small are also found numerically.

Danhua WangUniversity of [email protected]

Alejandro AcevesSouthern Methodist [email protected]

CP13

Weierstrass Traveling Wave Solutions for Dissipa-tive Equations

In this talk the effect of a small dissipation on waves is in-cluded to find exact solutions to the modified BBM equa-tion. We will use a general formalism based on Ince’s trans-formation to write the general solution in terms of Weier-strass ℘ functions, from which all the other known solutions

can be obtained via simplifying assumptions. This methodcan be applied to other similar dissipative equations.

Stefan C. MancasEmbry-Riddle Aeronautical University, Daytona [email protected]

CP13

Phase Wave Equation

I consider coupled oscillators which exhibit frequency syn-chronization without phase synchronization. The separa-tion of frequency and phase synchronizations leads to anew wave equation which can be called a phase wave equa-tion. I first explain the basic properties of the phase waveequation. Then I demonstrate that the phase wave equa-tion is generic and can support various kinds of wave whichinclude barbers pole, solitary wave, crawling motion etc.

Takashi OdagakiTokyo Denki [email protected]

CP13

Chiral Solitary Waves in Galilean Covariant FermiField Theories with Self-Interaction

A generalization of the Levy-Leblond equations for a (3 +1)-dimensional non-relativistic Fermi field for the case ofthe non-zero rest energy is considered. The self-interactionof the field is included and its rest mass is assumed todiffer from the inertial one. A positive chirality solitarywave solution with space oscillations in the x3-coordinateis constructed, the amplitude of the solution depending onthe rest energy. The wave’s energy and mass transferredthrough the unit area in the (x1, x2)-plane are calculated.Stability of the solution is discussed.

Fuad SaradzhevCentre for Science, Athabasca UniversityAthabasca, Alberta, [email protected]

CP13

Ultrashort Pulse Propagation in Periodic Media -Analysis and Novel Applications

We present a novel technique for manipulating short pulsesin periodically modulated media. Specifically, we show howto perform time-reversal, extreme pulse compression, ultra-fast switching and slow light. Our study includes an unusu-ally sophisticated multiple-scales analysis which is corrob-orated numerically with a full electrodynamic model anda simplified coupled mode theory. The technique can findapplications in any wave systems, especially in optics andacoustics. Finally, we review experimental tests of theseideas.

Yonatan SivanTel Aviv [email protected]

CP13

Transmission and Reflection of Airy Beams at AnInterface of Dielectric Media

Transmission and Reflection of Airy beams at an interfacebetween two diffusive linear-nonlinear dielectric media are

72 NW14 Abstracts

studied numerically and analytically. The beam dynam-ics is simulated by the beam propagation method. In thisstudy, the interesting cases of critical incidence of Brew-ster and total-internal-reflection angels are considered. Itis observed that the reflected beam nearly unaffected butshifted. Some interesting results will be presented in thistalk.

Rajah P. VaratharajahNorth Carolina A&T State [email protected]

CP13

Absolute Stabilization for the Axially MovingKirchhoff String with Nonlinear Boundary Feed-back Control

In this work, we consider the stabilization problem of thenonlinear axially moving Kirchhoff string using nonlinearboundary control. The nonlinear boundary control is thenegative feedback of the transverse velocity of the string atone end, which satisfies a polynomial type sector constrain.Employing the multiplier method, we establish explicit ex-ponential and polynomial stability for the Kirchhoff string.Simulation examples are presented based on finite elementmethod with Lagrange hat basis.

Yuhu Wu, Tielong ShenSophia [email protected], [email protected]

MS1

The Unified Transform for the NLS with t-PeriodicBoundary Conditions

The most challenging problem in the implementation of theso-called unified transform to the analysis of the nonlinearSchrodinger equation on the half-line is the characteriza-tion of the unknown boundary value in terms of the giveninitial and boundary conditions. For the so-called lineariz-able boundary conditions, this problem can be solved ex-plicitly. Furthermore, for non-linearizable boundary con-ditions which decay for large t, this problem can be largelybypassed in the sense that the unified transform yields use-ful asymptotic information for the large t behavior of thesolution. However, for the physically important case of pe-riodic boundary conditions, it is necessary to characterizethe unknown boundary value. Recent progress towards thesolution of this problem will be presented.

Athanassios S. FokasUniversity of [email protected]

MS1

The Initial Value Problem in Analytic Spacesof Nonlinear Evolution Equations with TravelingWave Solutions

We shall consider dispersive and weakly dispersive evolu-tion equations, which in addition to being integrable theyall have interesting traveling wave solutions and discusstheir Cauchy problem when the initial data are analytic.For dispersive equations, like KdV and cubic NLS, the solu-tion to the initial value problem with analytic initial datais analytic in the space variable and Gevrey in the timevariable. However, for weakly dispersive equations, likeCamassa-Holm type equations, the solution is analytic in

both variables.

Alex HimonasUniversity of Notre Dame, [email protected]

MS1

On Rigorous Aspects of the Unified TransformMethod

The unified transform method, introduced by Fokas in1997, produces novel solution formulae to boundary valueproblems for linear as well as integrable nonlinear equa-tions. For linear problems, in particular, this methodcan be employed even for non-separable or non-self-adjointproblems, where the classical solution techniques fail. Wewill discuss some rigorous aspects of these novel formulaein the case that the prescribed initial and boundary databelong to appropriate Sobolev spaces.

Dionyssis MantzavinosUniversity of Notre [email protected]

MS1

The Fokas Method for Interface Problems

Problems related to interfaces in different media arise fre-quently in applications and often are not solvable analyti-cally using classical approaches. In my talk I will show thatby adapting and expanding the Method of Fokas, solvingmany types of interface problems for the heat equation isnow possible. I will also show how to use these methodsfor an interface problem involving the linear Schrodingerequation and expand to mixed interface problems wheredifferent sides of the interface are governed by differingequations.

Natalie E. SheilsDepartment of Applied MathematicsUniversity of [email protected]

MS2

Motion in a Bose-Einstein Condensate: Vortices,Turbulence and Wakes

We show that an elliptical obstacle moving in a 2-dimensional Bose-Einstein condensate induces a wake re-sembling that seen in ordinary classical flows past a cylin-der. The wake consists of clusters of like-signed quantumvortices which are nucleated at the boundary of the ob-stacle. Vortex singularities in the inviscid superfluid thusmimic classical vortex patterns typical of viscous flows.Transitions from symmetric wake to time dependent Kar-man vortex street to turbulent wake are observed. Finally,we discuss these effects in view of current experiments inwhich oscillating wires, forks and grids are used to generateturbulence in superfluid helium.

Carlo F. BarenghiApplied Mathematics GroupNewcastle [email protected]

George Stagg, Nick G. ParkerNewcastle [email protected],

NW14 Abstracts 73

[email protected]

MS2

Intrinsic Photoconductivity of Ultracold Fermionsin An Optical Lattice

We report on the experimental observation of an analog toa persistent alternating photocurrent in an ultracold gas offermionic atoms in an optical lattice. The dynamics is in-duced and sustained by an external harmonic confinement.While particles in the excited band exhibit long-lived os-cillations with a momentum-dependent frequency, a strik-ingly different behavior is observed for holes in the lowestband. An initial fast collapse is followed by subsequentperiodic revivals. Both observations are fully explained bymapping the system onto a nonlinear pendulum.

Christoph BeckerInstitut fur LaserphysikUniversitat [email protected]

Jannes Heinze, Jasper Krauser, Nick Flaeschner, SoerenGoetze, Alexander Itin, Ludwig Mathey, Klaus SengstlockInstitut fur Laserphysik Universitat [email protected], [email protected], [email protected],[email protected], [email protected], [email protected],[email protected]

MS2

Pattern Formation in Solid State Condensates

In my talk I will discuss the phenomena observed in, andproperties of, microcavity excitonpolariton condensates.These are condensates of mixed light and matter, consist-ing of superpositions of photons in semiconductor micro-cavities and excitons in quantum wells. Because of the im-perfect confinement of the photon component, excitonpo-laritons have a finite lifetime, and have to be continuouslyre-populated. Therefore, excitonpolariton condensates liesomewhere between equilibrium BoseEinstein condensatesand lasers. I discuss the coherence properties of exciton-polariton condensates predicted theoretically and studiedexperimentally, and the wide variety of spatial structuresincluding quantised vortices, trapped states, states of aquantum harmonic oscillator, ring condensates and othercoherent structures. These patterns and their dynamicscan be reproduced through the solution of the complexGinzburg-Landau or the complex Swift-Hohenberg equa-tions. I will discuss to which extent these macroscopicquantum states can be understood as linear or nonlinearphenomena and what criteria can be applied to make sucha separation.

Natalia G. BerloffUniversity of [email protected]

MS2

Quantum Hall Effect and Transport Phenomena inLossy Photonic Lattices

We discuss properties of photonic cavities aligned in a formof a lattice. Because of the inherent loss of photons, thesteady-state configuration is achieved as a result of contin-uous gain and loss, which can theoretically be obtained

through solving an equation similar to the Schrodingerequation but with an imaginary term representing loss. Wediscuss how some transport properties, such as the quan-tum Hall effect, show themselves in such driven-dissipativesystems.

Tomoki OzawaDipartimento di FisicaUniversita di [email protected]

MS3

Asymptotic Stability for Nls with Nonlinear PointInteractions

We report on recent results concerning a Schrodinger Equa-tion with an attractive nonlinearity concentrated at apoint. In particular, we focus on the problem of the asymp-totic stability of the Ground States. We treat both cases ofa linearized evolution with or without bound states. Thisis a joint work with D. Noja (Milan) and C. Ortoleva (Mi-lan).

Riccardo AdamiUniversity of [email protected]

MS3

Scattering for Nonlinear Schrdinger Equations un-der Partial Harmonic Confinement

We consider the nonlinear Schrodinger equation under apartial quadratic confinement. We show that the globaldispersion corresponding to the direction(s) with no poten-tial is enough to prove global in time Strichartz estimates.We infer the existence of wave operators. Asymptotic com-pleteness stems from suitable Morawetz estimates, which inturn follow from the latest approach, applied to a marginalof the position density. This is a joint work with Paolo An-tonelli and Jorge Drumond Silva.

Remi CarlesCNRS & Universite Montpellier [email protected]

MS3

Some Collision Problems Related to NonlinearSchrdinger Equations

In this talk I will discuss a more qualitative lack of stabilityof several structures of solitary wave type. I will focus thisdescription on the nonlinear Schrdinger model, althoughthe proposed account of the dynamics can be adapted toseveral other models with unstable solitons.

Claudio MunozUniversity Paris [email protected]

MS3

On the Long-Time Behavior of NLS in the PartiallyPeriodic Setting

We present results on the Nonlinear Schroedinger equationposed in the partially periodic setting Rd ×T and we lookat the long-time behavior of the solutions. In particular weshall study theH1 scattering in the regime of nonlinearitieswhich are both L2-supercritical and energy subcritical. We

74 NW14 Abstracts

also present results related to the modified scattering forthe cubic NLS in the partially periodic setting R×Td.

Nicola ViscigliaUniversity of [email protected]

MS4

An Asymptotic Model for Small Amplitude Solu-tions to Newton’s Cradle

We study the dynamics of a one-dimensional lattice ofnonlinearly coupled oscillators. The class of problems ad-dressed include Newton’s cradle with Hertzian contact in-teractions. The Cauchy problem is studied yielding lowerbounds for the existence time. We then derive an asymp-totic model for small amplitude solutions over large times.This allows to prove the existence of breather-like solutionsto the initial model. We also estimate the maximal disper-sion of localized initial data.

Brigitte Bidegaray-FesquetCNRS and Grenoble University, [email protected]

Eric DumasInstitut Fourier, Universite Grenoble 1 and [email protected]

Guillaume JamesLaboratoire Jean Kuntzmann, Universite de Grenobleand [email protected]

MS4

Justification of Leading Order Quasicontinuum Ap-proximations of Strongly Nonlinear Lattices

After giving a brief introduction to the topic of granularcrystals, I will consider the leading order quasicontinuumlimits of a one-dimensional granular chain governed by theHertz contact law under precompression. The approximatemodel, a so-called p-system, which is derived in this limitis justified by establishing asymptotic bounds for the errorwith the help of energy estimates. The continuum modelpredicts the development of shock waves, which we inves-tigate with the aid of numerical simulations.

Christopher ChongUniversity of Massachusetts, [email protected]

Panayotis KevrekidisDepartment of Mathematics and StatisticsUniversity of [email protected]

Guido SchneiderUnviersity of [email protected]

MS4

Transitions from Energy Entrapment to EnergyTransport in the System of N Coupled GranularChains

In the present study we analyze the governing mechanisms

of transition from energy entrapment to energy transportin the system of N coupled, granular chains. Two distinctmechanisms leading to the breakdown of energy localiza-tion on the first and the second chains have been revealedand analyzed in the study. Using the regular multi-scaleasymptotic analysis along with the non-smooth temporaltransformation method (NSTT) we formulate the analyticcriteria for the formation of the inter-chain energy trans-port. Results of the analytical approximation are in a verygood correspondence with the results of numerical simula-tions of the full model.

Yuli StarosvetskyTechnion, Israel Institute of [email protected]

MS4

Acoustic Wave Filtering and Breather Formationin Coupled Granular Chains Embedded in MaterialMatrix

We present an experimental study of primary pulse trans-mission in coupled ordered granular chains embedded inelastic matrix under harmonic excitation. We find thatdepending on the magnitude and frequency of the appliedexcitation these strongly nonlinear dynamical systems mayeither support propagating pulses (in pass bands), or mayattenuate higher frequency harmonic components (in stopbands). Hence, these media act as tunable nonlinear acous-tic filters. In the transition between pass and stop bandsthese systems support breathers, in the form of weaklymodulated oscillating waves. These results are confirmedtheoretically and experimentally.

Alexander Vakakis, M. Arif Hasan, Sinhu Cho, D.Michael McFarland, Waltraud M. KrivenUniversity of [email protected], [email protected],[email protected], [email protected],[email protected]

MS5

Interfaces in a Random Environment

We review results on the qualitative behaviour of parabolicevolution equations with random coefficients which modelthe evolution of an interface which moves in a randomenvironment. The typical examples are randomly forcedmean curvature flow (with a forcing which depends onspace onlu) and related semi-linear models (random ob-stacle model).

Nicolas DirrCardiff School of MathematicsCardiff [email protected]

MS5

Not Available at Time of Publication


Gabriel J. LordHeriot-Watt [email protected]

MS5

Noise Induced State Transitions, Intermit-

NW14 Abstracts 75

tency and Universality in the Noisy Kuramoto-Sivashinsky Equation

We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS)equation in a regime close to the instability onset. Weshow that when the noise is highly degenerate, in the sensethat it acts only on the first stable mode, the solution of theKS equation undergoes several transitions between differ-ent states, including a critical on-off intermittent state thatis eventually stabilized as the noise strength is increased.Such noise-induced transitions can be completely charac-terized through critical exponents, obtaining that both theKS and the noisy Burgers equation belong to the same uni-versality class. The results of our numerical investigationsare explained rigorously using multiscale techniques.

Greg PavliotisImperial College [email protected]

MS5

Stability of Traveling Waves in Bistable Reaction-Diffusion Equations

Stability of traveling waves in stochastic bistable reaction-diffusion equations with both additive and multiplicativenoise is proven, using a variational approach based on func-tional inequalities. Explicit estimates on the rate of stabil-ity are derived that can be shown to be optimal in thespecial case of stochastic Nagumo equations. Our anal-ysis allows to derive a stochastic differential equation forthe motion of the wave front and a mathematical rigorousdecomposition of the full dynamics into the phase-shiftedtraveling wave and non-Gaussian fluctuations.

Wilhelm StannatTU [email protected]

MS6

Actin Polymerization and Subcellular MechanicsDrive Nonlocal Excitable Waves in Living Cells


Jun AllardUniversity of California, IrvineDepartment of [email protected]

MS6

Clock and Wavefront Model of Somitogenesis

The currently accepted interpretation of the clock andwavefront model of somitogenesis is that a posteriorly mov-ing molecular gradient sequentially slows the rate of clockoscillations, resulting in a spatial readout of temporal os-cillations. However, while molecular components of theclocks and wavefronts have now been identified in the pre-somitic mesoderm (PSM), there is not yet conclusive ev-idence demonstrating that the observed molecular wave-fronts act to slow clock oscillations. Here we present analternative formulation of the clock and wavefront modelin which oscillator coupling, already known to play a keyrole in oscillator synchronisation, plays a fundamentallyimportant role in the slowing of oscillations along the an-teriorposterior (AP) axis. Our model has three parame-ters that can be determined, in any given species, by the

measurement of three quantities: the clock period in theposterior PSM, somite length and the length of the PSM.A travelling wavefront, which slows oscillations along theAP axis, is an emergent feature of the model.

Ruth E. BakerUniversity of OxfordCentre for Mathematical [email protected]

MS6

Ca2+/calmodulin-Dependent Protein KinaseWaves in Heterogeneous Spiny Dendrites


Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]

MS6

Actin Nucleation Waves in Motile Cells


William R. HolmesUniversity of California, IrvineDepartment of [email protected]

MS7

Jet-Particle Methods for Incompressible Fluids

A Lagrangian model of ideal incompressible fluid flow isintroduced in which a kth order deformation is attachedto each particle. The data associated to the deformationgradient is formally represented as an internal degree offreedom within each particle. In particular, it is a gaugeassociated to the kth order jet-group of a point, and we re-fer to the particle as a k-jet particle. Through an infinite-dimensional reduction by symmetry, solutions may be ob-tained to the fluid equation by solving a finite dimensionalODE. The resulting ODE is then solvable using standardintegration schemes. Interesting behavior occurs when weconsider particle collisions. We find that collisions of a k-jet particles and an -jet particles yield (in infinite time) a(k + )-jet particle. This can be interpreted as a model ofthe energy cascade of an ideal incompressible fluid.

Colin CotterImperial [email protected].

Darryl D. Holm, Henry JacobsImperial College [email protected], [email protected]

MS7

Structure-preserving Discretization of Fluid Me-chanics

In this talk we will geometrically derive discrete equationsof motion for fluid dynamics from first principles. Our ap-proach uses a finite-dimensional Lie group to discretize thegroup of volume-preserving diffeomorphisms, and the dis-crete Euler equations are derived from a variational princi-ple with non-holonomic constraints. The resulting discrete

76 NW14 Abstracts

equations of motion induce a structure-preserving time in-tegrator with good long-term energy behavior, for which anexact discrete Kelvin circulation theorem holds. Our meth-ods can be used to derive structure-preserving integratorsfor many systems, such as equations of magnetohydrody-namics, complex fluids etc.

Dmitry PavlovImperial College [email protected]

MS7

Geometric Theory of Garden Hose Dynamics

Instability of flexible tubes conducting fluid, or ”gardenhose instability”, is a phenomenon both familiar from ev-eryday life and important for applications, and thereforehas been actively studied. In spite of its long history, manyunanswered questions remain, in particular, how to ad-dress a dynamically changing cross-section. We construct afully three dimensional, exact geometric theory of this phe-nomenon by coupling the dynamics of the elastic tube (left-invariant) with the motion of the fluid (right-invariant)with additional volume constraint. We also discuss theboundary conditions through an appropriate, Lagrange-d’Alembert’s like modification of the critical action prin-ciple. We show that the change of the cross-section affectsthe stability properties, derive a class of exact, fully nonlin-ear solutions of traveling wave type and (time permitting),discuss the results of experiments elucidating some impor-tant aspects of the dynamics.

Vakhtang PutkaradzeUniversity of [email protected]

MS7

Using Multi-Moment Vortex Methods to StudyMerger

We use a low order model to understand how two co-rotating vortices transition from a quasi-steady distancefrom each other to the rapid convective merger that occursafter diffusion causes the vortex core size to exceed somecritical fraction of the separation distance. This model wasderived from the recently developed Multi-Moment VortexMethod and provides several physical insights as well aspins down precisely what causes the very initial onset ofconvective merger.

David T. UminskyUniversity of San FranciscoDepartment of [email protected]

MS8

Inviscid Damping and the Asymptotic Stability ofPlanar Shear Flows in the 2D Euler Equations

We prove the asymptotic stability of shear flows close tothe planar, periodic Couette flow in the 2D incompressibleEuler equations. Specifically: given an initial perturbationof the Couette flow small in a suitable regularity class,the velocity converges strongly in L2 to a shear flow ast-¿infinity. The vorticity is mixed to small scales and ingeneral enstrophy is lost in the weak limit. Joint workwith Nader Masmoudi.

Jacob Bedrossian

Courant Institute of Mathematical SciencesNew York [email protected]

MS8

Large Deviations for Stochastic Partial DifferentialEquations with Applications in Planetary Atmo-sphere Dynamics

We will discuss several recent result for the computationof large deviation rate function for stochastic differentialequations, including the stochastic two-dimensional Eulerand Navier-Stokes equations, and quasi-geostrophic modelsthat describe planetary atmospheres. Both explicit resultsfor the quasi-potential expression and numerical compu-tations will be discussed. From those computations, wepredict non-equilibrium phase transitions and bistable sit-uations.

Freddy BouchetLaboratoire de PhysiqueENS de [email protected]

MS8

Center Manifolds and Taylor Disperson

Taylor dispersion, first described by G. Taylor in 1953, oc-curs when the diffusion of a solute in a long channel orpipe is enhanced by the background flow, in that the so-lute asymptotically approaches a form that solves a differ-ent diffusion equation (with larger diffusion coefficient, inan appropriate moving frame). By introducing scaling vari-ables, I’ll show how one can obtain this asymptotic formvia a center manifold reduction. This is joint work withMargaret Beck and C.E. Wayne.

Osman ChaudharyBoston UniversityDepartment of Mathematics and [email protected]

MS8

Pseudospectrum for Oseen Vortices Operators

Oseen vortices are self-similar solutions to the vorticityequation in R2. T.Gallay and C.E.Wayne proved in 2005that these solutions are stable for any value of the cir-culation Reynolds number. The linearization of the sys-tem around an Oseen vortex naturally gives rise to a non-self-adjoint operator. We shall discuss spectral and pseu-dospectral properties of the linearized operator in the fastrotation limit. In particular, we give some (optimal) resol-vent estimates along the imaginary axis.

Wen DengMathematical SciencesLund [email protected]

MS9

Mixed Boundary Value Problems for Stokes Flows:New Methods and Applications

Motivated by microfluidics applications where it is re-quired to manipulate viscous fluids at small scales wepresent some novel mathematical approaches to a varietyof mixed boundary value problems for biharmonic fields

NW14 Abstracts 77

arising therein. The methods, which are based on a formu-lation originally presented by Crowdy & Fokas [Proc. Roy.Soc. A, 460, (2004)], are general and have much widerapplicability in other areas.

Darren G. CrowdyImperial College [email protected]

MS9

The Nonlinear Schrdinger Equation with PeriodicBoundary Data

I will present some new results related to the initial-boundary value problem for the nonlinear Schrdinger equa-tion on the half-line with an asymptotically periodicboundary condition.

Jonatan LenellsDepartment of MathematicsBaylor Universityjonatan [email protected]

MS9

Well-Posedness and Spectral Representation ofLinear Initial-Boundary Value Problems

We study initial-boundary value problems for linearconstant-coefficient evolution equations on a finite 1-space,1-time domain. Classical separation of variables andFourier transform methods fail for all problems exceptthose of second order or those with very special boundaryconditions whereas the method of Fokas solves any suchwell-posed problem. We describe the well-posedness crite-ria and provide a functional-analytic view of the failure ofclassical methods and the success of Fokas’ method.

David SmithUniversity of [email protected]

MS9

A Retrospective Inverse Problem for the WaveEquation

A typical retrospective inverse problem is one where weattempt to recover the full solution to the heat equation,say on the whole line, given time series data at a specificlocation i.e. Dirichlet data. In this talk, I shall considerthis problem for the wave equation: given time-series dataat fixed spatial locations, can one recover the full solutionto the problem posed on the whole line? By using simplearguments based on Fokas’ method we shall obtain neces-sary conditions to recover the solution. Further employ-ing the global relations for the associated boundary-valueproblems we obtain a system of equations to solve for theinitial condition everywhere.

Vishal VasanDepartment of MathematicsThe Pennsylvania State University

[email protected]

MS10



Jean-Marc ChomazLADHYXEcole [email protected]

MS10

Dissection of Boussinesq Non-linear InteractionsUsing Intermediate Models

Nonlinear coupling among wave modes and vortical modesis dissected in order to probe the question: Can we dis-tinguish the wave-vortical interactions largely responsiblefor formation versus evolution of coherent, balanced struc-tures? It is well known that the quasi-geostrophic (QG)equations can be derived from the Boussinesq system ina non-perturbative way by ignoring wave interactions andconsidering vortical modes only. One qualitative differencebetween those two models is the lack of skewness in theQG dynamics. In this talk, non-perturbative intermediatemodels that include more and more classes of non-linearinteractions will be used to identify their role in differentqualitative properties of the Boussinesq system. Numericalresults will be shown to describe the effect of each class inthe transfer of energy between vortical modes and waves,transfer of energy (or the lack of it) between scales, forma-tion of vortices and skewness.

Gerardo Hernandez-DuenasDepartment of MathematicsUniversity of Wisconsin, [email protected]

Leslie SmithMathematics and Engineering PhysicsUniversity of Wisconsin, [email protected]

Samuel StechmannUniversity of Wisconsin - [email protected]

MS10

A Coupled Model of the Interactions Between In-ertial Waves and Turbulence in the Ocean

We derive a new model of the interactions between near-inertial waves (NIWs) and balanced motion in the oceanusing Generalised Lagrangian Mean theory and Whithamaveraging. In its simplest form, the model couples the well-known Young-Ben Jelloul model of NIWs with a quasi-geostrophic model of the balanced motion. The modelis Hamiltonian and conserves both energy and wave ac-tion. Analytic arguments and numerical simulations of themodel shed light on mechanisms of NIW-mean flow inter-actions in the ocean.

Jacques Vanneste, Jin-Han XieSchool of MathematicsUniversity of Edinburgh

78 NW14 Abstracts


MS10

Centrifugal, Barotropic and Baroclinic Instabili-ties of Isolated Ageostrophic Anticyclones in theTwo-layer Rotating Shallow Water Model and theirNonlinear Saturation

Instabilities of the isolated anticyclonic vortices in the 2-layer rotating shallow water model are studied at Rossbynumbers up to 2, with the main goal to understand theinterplay between the classical centrifugal instability andother possible ageostrophic instabilities. We find that dif-ferent types of instabilities with low azimuthal wavenum-bers exist, and may compete. In a wide range of parametersan asymmetric version of the standard centrifugal instabil-ity has larger growth rate than this latter. The dependenceof the instabilities on the parameters of the flow: Rossbyand Burger numbers, vertical shear, and the ratios of thelayers’ thicknesses and densities is investigated. The zonesof dominance of each instability are determined in the pa-rameter space. Nonlinear saturation of these instabilitiesis then studied with the help of a high-resolution finite-volume numerical scheme, by using the unstable modesidentified from the linear stability analysis as initial con-ditions. Differences in nonlinear development of the com-peting centrifugal and ageostrophic barotropic instabilitiesare exposed.

Vladimir Zeitlin, Noe LahayeENS/University of Paris 6, [email protected], [email protected]

MS11

Selection Principles for Semiclassical Flows overConical Singularities: Asymptotic and Computa-tional Investigation

When a pure state interacts strongly with conical singular-ities, there are several possible classical evolutions. Basedon recent rigorous results, we propose a selection princi-ple for the regularization of semiclassical asymptotics forSchroedinger equations with Lipschitz potentials. Employ-ing a solver with a posteriori error control, we generate rig-orous upper bounds for the error in our asymptotic approx-imation. For 1-dimensional problems without interference,we obtain compelling agreement between the regularizedasymptotics and the full solution. This allows the formu-lation of a conjecture for the validity of the regularizedasymptotics. Both the selection principle, and the compu-tation with a posteriori error control to check it, can beextended to the 1D Schroedinger-Poisson equation, wherethe non-linearity is also generated by a conical singularity.Existing work in the same spirit, and implications of ourapproach in that problem are briefly discussed.

Agisilaos AthanassoulisUniversity of [email protected]

MS11

Nonlinear Propagation of Coherent States ThroughAvoided Energy Level Crossing

We study the propagation of a coherent state for a one-dimensional system of two coupled Schrdinger equations inthe semi-classical limit. Couplings are induced by a cubicnonlinearity and a matrix-valued potential, whose eigenval-

ues present an ”avoided crossing” : at one given point, thegap between them reduces as the semi-classical parameterbecomes smaller. We show that when an initial coherentstate polarized along an eigenvector of the potential prop-agates through the avoided crossing point, there are tran-sitions between the modes at leading order. In the regimewe consider, we observe a nonlinear propagation far fromthe crossing region while the transition probability can becomputed with the linear Landau-Zener formula.

Lysianne HariUniversity [email protected]

MS11

Dispersive Estimates for Non-Autonomous Hamil-tonians and Applications to Nonlinear AsymptoticStability of Solitary Waves

The pioneering work of Soffer and Weinstein in the ’90introduced the method of controlling the nonlinearity bydispersive estimates of the linearized operator at a frozentime. It has now become a classical method to studyasymptotic stability of nonlinear waves and has shown thatthe actual dynamics shadows different solitary waves be-fore collapsing to one. What is less known is that themethod can be significantly improved if one obtains anduses dispersive estimates for the time dependent linearizeddynamics, i.e. the linearization is at the solitary waveshadowed at that moment and changes as the dynamicsmoves from one solitary wave to another. I will discusshow this new perspective has allowed us to tackle, for thefirst time, subcritical nonlinearities in Schrodinger equa-tions and to significantly reduce smoothness assumptionsin nonlinear Dirac equations. This is joint work with A.Zarnescu (U. Sussex, England), O. Mizrak (Mersin U.,Turkey), R. Skulkhu (Mahidol U., Thailand) and N. Bous-said (U. Franche-Comte, France).

Eduard KirrDepartment of MathematicsUniversity of Illinois at [email protected]

MS11

Dispersion and Long Time Evolution of CoherentStates

We consider the the semiclassical limit of solutions of thetime dependent Schrodinger equation with potential, andwith initial conditions given by coherent states. The evo-lution of the shape of a coherent state depends strongly onthe classical dynamics which emerges in the semiclassicallimit, and we use this dynamics to give precise estimateson how a coherent state disperses for large times and even-tually becomes a Lagrangian state. This can then be usedto transform a nonlinear Schrodinger equation into a newform in which the nonlinearity decays in time.

Roman SchubertUniversity of [email protected]

MS12

Granular Crystals at the Microscale

The nonlinear dynamics of a two-dimensional granularcrystal composed of 1 μm silica microspheres assembledon an elastic substrate are studied. The dynamics of the

NW14 Abstracts 79

system are shown to differ significantly from macroscalegranular media due to effects such as interparticle andparticle-substrate adhesion. High amplitude surface acous-tic waves are excited and measured in the coupled systemvia the laser-induced transient grating technique. The pho-toacoustic measurements are compared with our analyticalmodel and numerical simulations.

Nicholas BoechlerMassachusetts Institute of TechnologyDepartment of Mechanical [email protected]

MS12

Solitary Waves in a 1D Chain of Repelling Magnets

We study experimentally, numerically and theoretically thedynamics of a 1D discrete nonlinear lattice composed ofrepelling magnets. We demonstrate that such lattice sup-ports solitary waves with profile and propagation speed de-pending on the amplitude. The system belongs to the kindof nonlinear lattices studied in [Friesecke and Matthies,Physica D, 171(2002) 211-220] and exhibits sech2 profilein the low energy regime and atomic scale localization inthe high energy regime. Such systems may find potentialapplications in the design of novel devices for shock absorp-tion, energy localization and focusing. Furthermore, dueto the similarity of the magnetic potential with the poten-tials governing atomic forces, the system could be used fora better understanding of important problems in physicsand chemistry.

Miguel [email protected]

Andrea LeonardCell BiomechanicsUniversity of [email protected]

Chiara DaraioETH Zurich, Switzerland and California Institute of [email protected]

MS12

Disordered Granular Chains

I investigate the propagation and scattering of highly non-linear waves in disordered granular chains composed ofspheres that interact via Hertzian contact. Experimentsand numerical simulations both reveal the existence of twodifferent mechanisms of wave propagation. In low-disorderchains, one observes a decaying solitary pulse; beyond acritical level of disorder, the decay is faster and the wavetransmission becomes insensitive to the level of disorder.I will also compare results from different families of disor-dered arrangements.

Mason A. PorterUniversity of OxfordOxford Centre for Industrial and Applied [email protected]

MS12

Modulation of Nonlinear Waves in Woodpile

Phononic Crystals

We present experimental and numerical studies on themodulational effect of nonlinear waves in woodpilephononic crystals composed of slender, cylindrical ele-ments. We find that various patterns of wave modulationand attenuation can be achieved in woodpile architecturesassociated with their natural bending modes. The numer-ical results based on finite element and discrete elementmethods corroborate experimental results well. Woodpilephononic crystals can offer new testbed for manipulatingnonlinear wave propagation.

Jinkyu Yang, Eunho KimUniversity of [email protected], [email protected]

MS13

Determining Wave Stability Via the Maslov Index

The Maslov index is a symplecto-geometric invariant thatcounts signed intersections of Lagrangian subspaces. It wasrecently shown that the Maslov index can be used to com-pute Morse indices of selfadjoint, elliptic boundary valueproblems on star-shaped domains. We extend these resultsto bounded domains with arbitrary geometry, and discusssome applications to the stability of nonlinear waves.

Graham CoxUniversity of North CarolinaChapel Hill, [email protected]

Chris JonesUniversity of North Carolina-Chapel [email protected]

Jeremy L. MarzuolaDepartment of MathematicsUniversity of North Carolina, Chapel [email protected]

MS13

The Krein Matrix for Quadratic Eigenvalue Prob-lems

In order to understand spectral stability for Hamiltoniansystems, there are two types of eigenvalues that need tobe found: those with positive real part, and those purelyimaginary ones with negative Krein signature. The formercan be easily identified visually; however, the latter can-not. Knowing the signature of an eigenvalue is necessaryin order to determine which eigenvalues can contribute toa Hamiltonian-Hopf bifurcation. The Krein matrix is ameromorphic matrix which can be used to not only findeigenvalues, but it can be used to graphically determinethe Krein signature of purely imaginary eigenvalues. Wewill discuss its construction, and how it can be used inconjunction with the Hamiltonian-Krein instability indextheory in order to study Hamiltonian eigenvalue problems.

Todd KapitulaCalvin CollegeDept of Math & [email protected]

Shamuel Auyeung, Eric YuCalvin College

80 NW14 Abstracts


MS13

On the Maslov Index for Periodic and for Multidi-mensional Problems

In this talk we discuss some recent results on connectionsbetween the Maslov and the Morse indices for differentialoperators. The Morse index is a spectral quantity definedas the number of negative eigenvalues counting multiplici-ties while the Maslov index is a geometric characteristic de-fined as the signed number of intersections of a path in thespace of Lagrangian planes with the train of a given plane.The problem of relating these two quantities is rooted inSturm’s Theory and has a long history going back to theclassical work by Arnold, Bott, Duistermaat, Smale, andto a more recent paper by Deng and Jones. Two situa-tions will be addressed: First, the case when the differ-ential operator is a Schroedinger operator equipped withtheta-periodic boundary conditions, and second, when theSchroedinger operators are acting on a family of multi-dimensional domains obtained by shrinking a star-shapeddomain to a point and are equipped with either Dirichlet orquite general Robbin boundary conditions. This is a jointwork with G. Cox, C. Jones, R. Marangell, A. Sukhtayev,and S. Sukhtaiev.

Yuri LatushkinDepartment of MathematicsUniversity of [email protected]

MS13

Computing the Maslov Index

We address the problem of computing the Maslov indexfor large linear symplectic systems on the real line. TheMaslov index measures the signed intersections (with agiven reference plane) of a path of Lagrangian planes. Thenatural chart parameterization for the Grassmannian ofLagrangian planes is the space of real symmetric matrices.Linear system evolution induces a Riccati evolution in thechart. For large order systems this is a practical approachas the computational complexity is quadratic in the order.The Riccati solutions, however, also exhibit singularites(which are traversed by changing charts). Our new resultsinvolve characterizing these Riccati singularities and twotrace formulae for the Maslov index. We demonstrate theeffectiveness of these approaches by applying them to alarge eigenvalue problem. We also discuss the extension ofthe Maslov index to the infinite dimensional case.

Simon MalhamHeriot-Watt [email protected]

Margaret BeckBoston University and Heriot-Watt [email protected]

MS14

Spatial Patterns on Time-Dependent Domains:Convective and Dilution Effects

We explore the key differences in the near-critical behav-ior between extended systems on time-fixed and time-dependent spatial domains, with particular emphasis onthe effects of convection and dilution. As a paradigm, we

take the Swift-Hohenberg equation, which is the simplestnonlinear model with a finite critical wavenumber, and useit to study dynamic pattern formation and evolution ontime-dependent spatial domains. In particular, we discussthe effects of a time-dependent domain on the stability ofspatially homogeneous and spatially periodic base states,and explore the effects of convection and dilution on theEckhaus instability of periodic states. We show that thisinstability is repeatedly triggered as the domain grows andthat it leads to phase slips that are responsible for the in-sertion of additional wavelengths required to maintain apreferred wavenumber. This behavior is captured by anevolution equation for the pattern wavenumber that canbe derived from a generalized complex Ginzburg-Landauequation describing the nonlinear evolution of the patternamplitude on time-dependent domains in the presence ofconvection and dilution. The results are compared withthose on fixed domains.

Rouslan KrechetnikovDepartment of Mechanical EngineeringUniversity of California at Santa [email protected]

Edgar KnoblochUniversity of California at BerkeleyDept of [email protected]

MS14

Recent Advances in Pattern Formation on Grow-ing and Evolving Surfaces: Theory, Numerics andApplications

In this talk I will present theoretical results on the sta-bility analysis of reaction-diffusion systems on evolvingdomains. There are two fundamental biological differ-ences between the Turing conditions on fixed and grow-ing domains, namely: (i) we need not enforce cross norpure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growingbiological system is no longer a requirement. Our theoreti-cal findings are confirmed and reinforced by numerical sim-ulations for the special cases of isotropic linear, exponentialand logistic growth profiles. In particular we illustrate anexample of a reaction-diffusion system which cannot ex-hibit a diffusively-driven instability on a fixed domain butis unstable in the presence of slow growth. Generalisationsto reaction-diffusion systems with cross-diffusion as well asresults on evolving surfaces will be presented.

Anotida MadzvamuseUniversity of SussexDept of [email protected]

MS14

Effect of Dissolution-Driven Convection on thePartial Mixing Between CO2 and Hydrocarbons OrReactive Solutions

Reducing greenhouse gas emissions to mitigate climatechange is one of the most timely and important challengesin environmental and energy-related issues. Subsurfacecarbon sequestration has emerged as a promising solutionto the problem of rising atmospheric carbon dioxide (CO2)levels. However, the question remains as to how the effi-ciency and safety of such a sequestration process depend onthe physical and chemical characteristics of the storage site.

NW14 Abstracts 81

This question is emblematic of the need to better under-stand the dynamics of CO2 in subsurface formations whereit is known to dissolve into the pre-existing fluid (hydro-carbons in depleted oil fields and brine in saline aquifers).This dissolution, known to improve the safety of the se-questration by reducing the risks of leaks of CO2 to theatmosphere, leads to an increase of the density of the liq-uid phase in the gravity field, thereby leading to naturalconvection. We aim to describe the mass transport betweenthe non-equilibrium gas and liquid phases of a binary mix-ture. Our model accounts for the motion of the interface,diffusion and convective mass transport due to compress-ibility, non ideality, and natural convection. We show thatnatural convection influences the mixing time drastically.On the basis of a linear stability analysis of a simplifiedmodel, we also show that a chemical reaction of CO2 witha dissolved chemical species can either enhance or decreasethe amplitude of the convective dissolution compared tothe non reactive case. On this basis, we classify the variouspossible cases and identify the parameters that could in-fluence the dissolution-driven convection in the subsurfaceformations, and thus impact the safety of carbon seques-tration.

Laurence RongyUniversite libre de [email protected]

MS14

Modelling and Simulation of Biological PatternFormation on Evolving Surfaces

We investigate models for biological pattern formation viareaction-diffusion systems posed on evolving surfaces. Thenonlinear reaction kinetics inherent in the models and theevolution of the surface mean that analytical solutions aregenerally unavailable and numerical simulations are neces-sary. We discuss numerical simulation of the model equa-tions by finite elements and focus on applications to cellmotility, chemotaxis and skin pigment pattern formation.

Chandrashekar VenkataramanUniversity of [email protected]

MS15

Stability of mKdV Breathers in the Energy Space

In this talk I will show some recent results about the H1

stability of breather solutions of mKdV. I will also presentBacklund transformations for the mKdV and I will explainhow we use them as a technical tool to get stability at thelevel of H1 regularity.

Miguel AlejoIMPA, [email protected]

MS15

On the Interaction of Nonlinear Schrodinger Soli-tary Waves

The aim of this talk is go give a brief account of someinteraction problems involving nonlinear solitary waves forthe Schrodinger equation, where the nonlinearity is eitherintegrable or non integrable. We will give a qualitativedescription of the involved dynamics.

Claudio Munoz

University Paris [email protected]

MS15

On the Dressing Method for Discrete IntegrableSystems

This talk will discuss the discrete analogue of the dressingmethod for continuous and discrete integrable systems. Wewill show how, starting from appropriate matrix Riemann-Hilbert problems, one can derive a number of completelyintegrable nonlinear differential-difference systems of equa-tions, together with their associated Lax pairs.

Qiao WangState University of New York at [email protected]

Gino BiondiniState University of New York at BuffaloDepartment of [email protected]

MS15

Stability of Line Standing Waves Near the Bifur-cation Point for Nonlinear Schrodinger Equation

We consider the transverse instability for nonlinearSchrodinger equation. One dimensional nonlinearSchrodinger equation has a stable soliton. Here, we regardthis soliton as a line soliton of two dimensional nonlinearSchrodinger equation on the periodic boundary conditionin the transverse direction with the period 2πL. Roussetand Tzvetkov showed that there exists the critical period2πL∗ such that the line soliton is stable for L < L∗ andthe line soliton is unstable for L > L∗. In this talk, we willpresent the transverse instability in the degenerate caseL = L∗ and the relation between the stability and the bi-furcation.

Yohei YamazakiKyoto University Kyoto, [email protected]

MS16

Phase Mixing and Hydrodynamic Stability

Phase mixing is thought to play an important role in thestability of certain coherent structures in inviscid fluid dy-namics and collisionless kinetic theory. However, math-ematically rigorous nonlinear stability results have beensomewhat elusive. We will discuss some recent advances onthis topic including a simplified proof of nonlinear Landaudamping in the Vlasov equations joint with Nader Mas-moudi and Clement Mouhot and the asymptotic stabilityof shear flows in 2D ideal fluids joint with Nader Masmoudi.

Jacob BedrossianCourant Institute of Mathematical SciencesNew York [email protected]

MS16

Reaction-Diffusion Equations with Spatially Dis-tributed Hysteresis

We consider continuous and discrete reaction-diffusionequations with hysteresis which is given at every spatial

82 NW14 Abstracts

point. Such equations arise when one describes hystereticinteraction between several diffusive and nondiffusive sub-stances. In the talk, we will discuss mechanisms of ap-pearing global and local spatio-temporal patterns due tohysteresis as well as their interconnection. This is a jointwork with Sergey Tikhomirov.

Pavel GurevichFreie Universitat [email protected]

MS16

Waves Through Lattices with Impurities

We consider scalar lattice differential equations posed onsquare lattices in two space dimensions. Under certain nat-ural conditions we show that wave-like solutions exist whenobstacles (characterized by “holes’) are present in the lat-tice. Our work generalizes to the discrete spatial settingthe results obtained by Berestycki, Hamel and Matano forthe propagation of waves around obstacles in continuousspatial domains.

Hermen Jan HupkesUniversity of LeidenMathematical [email protected]

Aaron HoffmanFranklin W. Olin College of [email protected]

Erik Van VleckDepartment of MathematicsUniversity of [email protected]

MS16

Using Graph Limits for Studying Dynamics ofLarge Networks

The theory of graph limits uses analytical methods for de-scribing structural properties of large graphs. We discusssome applications of this theory to constructing and justi-fying continuum limits and to studying stability of spatialpatterns of nonlocally coupled dynamical systems.

Georgi S. MedvedevDrexel [email protected]

MS17

A New Approach for Linear Elliptic BoundaryValue Problems

We will discuss the functional analytic foundations that un-derline Fokas’ unified approach to elliptic boundary valueproblems. It will be demonstrated that the global relationcompletely characterizes the Dirichlet-Neumann map fora large class of elliptic boundary value problems. A de-tailed treatment of linear elliptic boundary value problemson convex polygons will be presented and we will discussthe numerical implementation of the unified method in thiscase.

Anthony AshtonUniversity of Cambridge

[email protected]

MS17

Initial-Boundary-Value Problems for NonlinearWave Equations

The lecture will focus upon both the motivation and someof the recent analysis of boundary-value problems for non-linear, dispersive wave equations.

Jerry BonaUniversity of Illinois at [email protected]

MS17

The Effect of Boundary Conditions on Linear andNonlinear Waves

In this talk, I will discuss the effect of boundary conditionson the solvability of PDEs that have formally an integrablestructure, in the sense of possessing a Lax pair. Manyof these PDEs arise in wave propagation phenomena, andboundary value problems for these models are very impor-tant in applications. I will discuss the extent to whichgeneral approaches that are successful for solving the ini-tial value problem extend to the solution of boundary valueproblem. I will survey the solution of specific examples ofintegrable PDE, linear and nonlinear. The linear theoryis joint work with David Smith. For the nonlinear case, Iwill discuss boundary conditions that yield boundary valueproblems that are fully integrable, in particular recent jointresults with Thanasis Fokas and Jonatan Lenells on thesolution of boundary value problems for the elliptic sine-Gordon equation.

Beatrice PelloniUniversity of Reading, [email protected]

MS18

A Dynamical Scheme for Prescribing MesoscaleEddy Diffusivity in the Ocean

The resolution of the oceanic component of climate modelswill soon enter a regime where quasigeostrophic dynam-ics dominate. This talk will introduce a numerical schemefor dynamically adjusting the eddy diffusivity and viscos-ity of these models in a way that is appropriate for quasi-geostrophic motion at the gridscale. This scheme is in-spired by subgrid modeling techniques that are common in3D Large Eddy Simulation (e.g. Smagorinsky), but whichare not appropriate for climate-scale flows.

Scott BachmanDAMPTUniversity of [email protected]

Baylor Fox-KemperBrown [email protected]

MS18

On Resurging a Bore-Soliton-Spash

We were able to create an anomalously high rogue wavesplash in a water wave channel with a convergence involv-ing a bore and solitons, and we could control it. Unex-

NW14 Abstracts 83

pectedly, this man-made extreme or rogue wave is relatedto rogue waves in multidirectional seas, solutions of theKP-equation, tsunami run-up into coastal valleys, and cer-tain wave-energy devices, as we will show. Some steps to-wards the mathematical and numerical modeling of thisbore-soliton-splash will be discussed, including accurateconservative discretizations of water waves, and a single-phase mixture theory for air- and water in an approximatemodel for intermittent wave breaking.

Onno BokhoveSchool of MathematicsUniversity of [email protected]

MS18

A Strange Gas? Revisiting the Point Vortex Modelto Understand the Condensation Process in Two-Dimensional and Quasi-Geostrophic Turbulence

The statistical mechanics of a system of point vortices in-teracting in a bounded two-dimensional domain is revis-ited. It is shown that the familiar sinh-Poisson theory isincomplete, and describes the behaviour only for inversetemperatures below a critical value (β < βc), when the‘gas’ of point vortices has ‘condensed’ generating a meancirculation. For β > βc a theory of fluctuations, recentlygeneralised by the authors, is shown to describe the ‘uncon-densed’ state. Behaviour near the critical value is investi-gated using statistical sampling and DNS. The implicationsfor the behavior of unforced two-dimensional Navier-Stokesturbulence, magnetized plasmas, and superfluids are dis-cussed, and it is shown that the theory extends easily torelated problem of quasi-geostrophic vorticity dynamics.

Gavin [email protected]

MS18

Cloud-Edge Dynamics and Mysterious Holes in theSky

A holepunch cloud is a curious atmospheric phenomenonwhere a disturbance in a thin cloud layer, as can be causedby an ascending aircraft, leaves behind a growing circularhole of clear air. Observed since the dawn of aviation, onlyvery recently has the holepunch feature been simulated ina full-physics numerical weather model. Although the ini-tiation process has been clearly attributed to ice crystalformation, we explain that the continued expansion of thehole is a travelling front between two phases of moist air— unsaturated and weakly-stratified (clear) intruding intosaturated and moist-neutral (cloudy). Furthermore ourfluid model, a non-hyperbolic conservation law system, il-lustrates an unusual example of a travelling discontinuitythat satisfies the Rankine-Hugoniot conditions, yet existsdespite the absence of underlying characteristics.

David [email protected]@sfu.ca

MS19

Invariant Gibbs Measures for NLS on the Real Line

We discuss invariant Gibbs measures for NLS on the realline. Previously, Bourgain ’00 considered this problem andproved uniqueness of solutions to (sub-)cubic NLS with

the Gibbs measure as initial data. By viewing such ini-tial data as a diffusion process in x, we extend this resultto (sub-)quintic NLS. Moreover, we identify the limitingGibbs measure on the real line and show its invariance.

Tadahiro OhUniversity of [email protected]

MS19

Two-soliton Solutions to a Focusing Cubic Half-wave Equation on R

In this talk we discuss work in progress regarding a nonlo-cal focusing cubic half-wave equation. Evolution problemswith nonlocal dispersion naturally arise in physics as mod-els for wave turbulence and gravitational collapse. Thegoal of the present work is to construct asymptotic global-in-time two-soliton solutions and to discuss their behaviourin terms of growth of high Sobolev norms. The talk is basedon joint work with P. Gerard (Orsay, France), E. Lenzmann(Basel, Switzerland), and P. Raphael (Nice, France).

Oana PocovnicuInstitute for Advanced Studies, [email protected]

MS19

Going Beyond the Threshold: Scattering vs. Blow-up Dichotomy in the Focusing NLS Equation

We study the focusing nonlinear Schrodinger equationin RN , in the L2-supercritical regime with finite energyand finite variance initial data and investigate solutionsabove the energy (or mass-energy) threshold. We extendthe known scattering versus blow-up dichotomy above themass-energy threshold for finite variance solutions in theenergy-subcritical and energy-critical regimes, obtainingscattering and blow-up criteria for solutions with arbitrarylarge mass and energy. This is a joint work with T. Duy-ckaerts.

Svetlana RoudenkoGeorge Washington [email protected]

MS19

Dispersive Blow-Up in Schrdinger Type Equations

We review results from a recent joint paper together withJ. Bona, J. C. Saut, and G. Ponce on the possibility offinite-time, dispersive blow up for nonlinear equations ofSchroedinger type. This mathematical phenomena is one ofthe conceivable explanations for oceanic and optical roguewaves. We extend the existing results in the literaturein several aspects. In one direction, the theory is broad-ened to include the Davey-Stewartson and Gross-Pitaevskiiequations. In another, dispersive blow up is shown toobtain for nonlinear Schroedinger equations in spatial di-mensions larger than one and for more general power-lawnonlinearities. As a by-product of our analysis, a sharpglobal smoothing estimate for the integral term appearingin Duhamels formula is obtained.

Christof SparberUniversity of Illinois at Chicago

84 NW14 Abstracts

[email protected]

MS20

Kerr Optical Frequency Combs: from FundamentalTheory to Engineering Applications

We present the recent developments on the topic of Kerroptical frequency comb generation using whispering gallerymode resonators. These combs have are expected to pro-vide optical signals with exceptional amplitude and phasestability. We discuss recent theoretical developments whichare compared with numerical simulations and experimentalmeasurements. The technological interest of these combsfor various microwave photonics applications is also re-viewed.

Yanne ChemboOptics department, FEMTO-ST Institute, Besancon,[email protected]

MS20

From Microresonator Combs to Solitons

Microresonator based Kerr combs open the way for novelcompact photonic devices. This promise is supported bypredicted and recently experimentally demonstrated con-trolled transition from chaotic to phase locked combs asso-ciated with temporal solitons. We studied experimentallyand in systematic numerical simulation the correlation be-tween mode structure and comb dynamics. We found thatsolitons may appear in presence of mode coupling inducedavoided crossings, only if affected modes are sufficiently farfrom the pump frequency.

Michael GorodetskyFaculty of PhysicsM.V.Lomonosov Moscow State [email protected]

MS20

Pulse Energy Enhancement of Mode Locked FiberLaser by Cascading Nonlinear Polarization Rota-tion

The periodic response curve of mode locked fiber laser withnonlinear polarization rotation limits the single pulse en-ergy in the laser cavity by triggering multi-pulse lasing. Wepropose to engineer the effective response curve of the fibercavity by cascading multiple stages of nonlinear polariza-tion rotation schemes in fiber cavity which can enhance thesingle pulse energy in the cavity by improving the thresh-old of multi-pulsing with the combination of the multipleresponse curves.

Feng LiDept. of Electronic and Information EngineeringHong Kong Polytechnic [email protected]

J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]

P. K. Alex WaiHong Kong Polytechnic UniversityDept. of Electronic and Information Engineering

[email protected]

MS20

Modelocking Quantum Cascade Lasers UsingQuantum Coherent Saturable Absorption

Experimental efforts to create short, stable mid-infraredpulses using quantum cascade lasers (QCLs) have notbeen successful to date. Time-evolving, strong spatialhole-burning due to very fast gain recovery hinders mode-locking. We show that two-section quantum cascade laserscan be designed in which one of the sections acts as aquantum coherent absorbing medium, so that spatial hole-burning is suppressed and ultra-short pulses on the orderof 100 fs can be obtained.

Muhammad TalukderDepartment of Electrical and Electronic EngineeringBangladesh University of Engineering and [email protected]

Curtis R. MenyukUniversity of Maryland Baltimore [email protected]

MS21

Stability and Computation of Interacting Nonlin-ear Waves

We consider solutions of nonlinear reaction diffusion equa-tions composed of several localized waves which interactstrongly or weakly. We propose an extension of the freez-ing method which generates multiple coordinate frames.In these frames single waves stabilize independently whilestill keeping their nonlinear interaction. Asymptotic sta-bility of the decomposition system is shown in one space di-mension and numerical experiments are provided for bothweakly and strongly interacting waves in dimensions oneand higher.

Wolf-Juergen BeynBielefeld [email protected]

MS21

Stability of Fronts in Spatially InhomogeneousWave Equations

Model equations describing waves in anisotropic mediaor media with imperfections usually have inhomogeneousterms. This talk considers the effects of (non-local) inho-mogeneities on fronts and solitary waves in nonlinear waveequations. Inhomogeneities break the translational sym-metry and travelling waves are no longer natural solutions.Instead, the travelling waves tend to interact with the inho-mogeneity and get trapped, reflected, or slowed down. Theunderlying Hamiltonian structure of the wave equation al-lows for a rich family of stationary front solutions and theenergy densities inside the inhomogeneities provide s nat-ural parametrization for these solutions. In this talk, wewill show that changes of stability can only occur at criti-cal points of the length of the inhomogeneity as a functionof these energy densities and we give a necessary and suffi-cient criterion for the change of stability. We will illustratethe results with an example related to a Josephson junc-tion system with a finite length inhomogeneity associatedwith variations in the Josephson tunneling critical current.

NW14 Abstracts 85

Gianne DerksUniversity of SurreyDepartment of [email protected]

Christopher KnightDepartment of MathematicsUniversity of [email protected]

Arjen DoelmanMathematisch [email protected]

Hadi SusantoThe University of NottinghamUnited [email protected]

MS21

Spectral Analysis for Transition Front Solutions inMultidimensional Cahn-Hilliard Systems

We consider the spectrum associated with the linear oper-ator obtained when a Cahn-Hilliard system on R

n is lin-earized about a planar transition front solution. In thecase of single Cahn-Hilliard equations on R

n, it’s knownthat under general physical conditions the leading eigen-value moves into the negative real half plane at a rate |ξ|3,where ξ is the Fourier transform variable correspondingwith components transverse to the wave. Moveover, it hasrecently been verified that for single equations this spectralbehavior implies nonlinear stability. In this talk, I’ll dis-cuss recent results in which it is shown that this cubic ratelaw continues to hold for a broad range of multidimensionalCahn-Hilliard systems.

Peter HowardDepartment of MathematicsTexas A&M [email protected]

MS21

A Geometric Approach to Counting Eigenvalues:The Evans Function in Some Cellular TransportModels

This talk will focus on some geometric techniques in Evansfunction computations. The aim is to show how such meth-ods can 1) facilitate spectral calculations, and 2) describedynamical properties via said spectral calculations. Theapplication in mind is for systems of travelling fronts incellular transport models, specifically those describing tu-mour invasion and wound healing.

Robert MarangellThe University of [email protected]

MS22

Front Propagation in Bacterial Suspensions


Ray E. GoldsteinUniversity of Cambridge

Department of Applied Mathematics and [email protected]

MS22

Contagion Shocks in One Dimension

We consider an agent-based model of emotional contagioncoupled with motion in one dimension that has recentlybeen studied in the computer science community. Themodel involves movement with speed proportional to a“fear’ variable that undergoes a temporal consensus av-eraging with other nearby agents. We study the effect ofRiemann initial data for this problem, leading to shockdynamics that are studied both within the agent-basedmodel as well as in a continuum limit. We examine themodel under distinguished limits as the characteristic con-tagion interaction distance and the interaction timescaleboth approach zero. Here, we observe a threshold for theinteraction distance vs. interaction timescale that producesqualitatively different behavior for the system - in one caseparticle paths do not cross and there is a natural Eule-rian limit involving nonlocal interactions and in the othercase particle paths can cross and one may consider only akinetic model in the continuum limit.

Martin ShortGeorgia [email protected]

Andrea L. BertozziUCLA Department of [email protected]

Li Wang, Jesus RosadoUCLA [email protected], [email protected]

MS22

Agent-Based and Continuum Models for the For-mation of Stripes in Zebrafish

Zebrafish (Danio rerio), a small fish with black and yellowstripes, has the ability to regenerate its stripes in responseto growth or artificial disturbance. We simulate past laserablation experiments using discrete (agent-based) and con-tinuum (nonlocal conservation law) models. Both modelsconsider two cell types diffusing and reacting based on rulesof short range attraction and long range repulsion. Ourresults suggest that the radius of interaction is a key de-terminant of stripe formation.

Alexandria Volkening, Bjorn SandstedeBrown Universityalexandria [email protected],bjorn [email protected]

MS22

Co-Dimension One Self-Assembly


James von BrechtUniversity of California, Los Angeles

86 NW14 Abstracts

[email protected]

MS23

Geometric Wave Equations with Multi-componentSolitons

I will survey some recent work deriving integrable geomet-ric wave equations that are generalizations of Schrodingermap equations and their KdV analogs, as well as a ge-ometric map version of integrable Camassa-Holm typeequations. Through a generalized Hasimoto transforma-tion, these geometric map equations are related to multi-component integrable systems which have soliton or peak-on solutions.

Stephen AncoDepartment of MathematicsBrock [email protected]

MS23

The Analysis of a Class of Integrable EvolutionEquations

We shall consider a class of nonlinearevolution equa-tions that are integrable and discuss their analytic prop-erties,including the existence of peakon traveling wavesolutions, well-posedness, ill-posedness and the stabilityof their data-to-solution map. This class includes theCamassa-Holm equation, the Degasperis-Procesiequation,the Novikovequation,and the Fokas-Olver-Rosenau-Qiaoequation.The integrabilityof these equations has beenstud-ied in a unified way by V. Novikov.

Alex HimonasUniversity of Notre Dame, [email protected]

MS23

Integrable Equations in 3D: Deformations of Dis-persionless Limits

Classification of integrable systems remains as a topic ofactive research from the beginning of soliton theory. Nu-merous classification results are obtained in 1 + 1 dimen-sions by means of the symmetry approach. Although thesymmetry approach is also applicable to 2 + 1-dimensionalsystems, one encounters additional difficulties due to theappearance of nonlocal variables. There are several tech-niques to tackle the problem (e.g. the perturbative symme-try approach). In the perturbative symmetry approach onestarts with a linear equation having a degenerate disper-sion law and reconstructs the allowed nonlinearity. In thistalk we present a novel perturbative approach to the clas-sification problem. Based on the method hydrodynamicreductions, we first classify integrable quasilinear systemswhich may potentially occur as dispersionless limits of inte-grable 2 + 1-dimensional soliton equations. Subsequentlywe construct dispersive deformations preserving integrabil-ity deforming the hyrdrodynamic reductions by dispersivedeformations and requiring that all hydrodynamic reduc-tions of the dispersionless limit will be inherited by thecorresponding dispersive counterpart. The method also al-lows to effectively reconstruct Lax representations of thedeformed systems. We present various classification resultsobtained in the frame of the new approach, e.g. the clas-sification of scalar 2+1-dimensional equations generaliz-ing KP, BKP/CKP, the classification of Davey-Stewartson

type systems as well as various classifications of 2 + 1-dimensional differential-difference equations. The talk isbased on joint work with E. Ferapontov, A. Moro, B. Huardand I. Roustemoglou.

Vladimir NovikovLoughborough University, [email protected]

MS23

Well Posedness and Breakdown for Cauchy Prob-lems of Integrable Equations

We will discuss well posedness and breakdown results forsome integrable equations that can be derived as Euler-Arnold equations.

Feride TiglayOhio State University, [email protected]

MS24

A Spectral Theory of Linear Operators on aGelfand Triplet and Its Application to the Dynam-ics of Coupled Oscillators

The Kuramoto model is a system of ordinary differentialequations for describing synchronization phenomena de-fined as a coupled phase oscillators. In this talk, an infinitedimensional Kuramoto model is considered. Kuramoto’sconjecture on a bifurcation diagram of the system will beproved with the aid of a new spectral theory of linear op-erators based on Gelfand triplets.

Hayato ChibaInstitute of Mathematics for IndustryKyushu [email protected]

MS24

Pacemakers in a Large Array of Oscillators withNonlocal Coupling

We model pacemaker effects in a 1 dimensional array of os-cillators with nonlocal coupling via an algebraically local-ized heterogeneity. We assume the oscillators obey simplephase dynamics and that the array is large enough so thatit can be approximated by a continuous nonlocal evolutionequation. We concentrate on the case of heterogeneitieswith negative average and show that steady solutions to thenonlocal problem exist. In particular, we show that theseheterogeneities act as a wave source, sending out waves inthe far field. This effect is not possible in 3 dimensionalsystems, such as the complex Ginzburg-Landau equation,where the wavenumber of weak sources decays at infinity.To obtain our results we use a series of isomorphisms torelate the nonlocal problem to the viscous eikonal equa-tion. The linearization about the constant solution resultsin an operator, L, which is not Fredholm in regular Sobolevspaces. We show that when viewed in the setting of Kon-dratiev spaces the operator, L, is Fredholm. These spacescan be described as Sobolev spaces with algebraic weightsthat increase in degree with each derivative.

Gabriela JaramilloUniversity of Minnesota

NW14 Abstracts 87

[email protected]

MS24

From Particle to Kinetic and Hydrodynamic Mod-els of Flocking

In nature, one can find many species who’s combined inter-action give rise to large scale coherent structures withoutany force or leader guiding the interaction. The typicalexamples of such dynamics are flocking of birds, schools offish, or insect swarms. In this talk, we will consider some ofthe models proposed to capture such interaction. We shallstart at the level of particles and from there derive kineticand hydrodynamic models. The main novelty of the talkis that all passages will be made using rigorous arguments.From particles to kinetic models, convergence is measuredin Wasserstein distance, while from kinetic to hydrody-namic models, convergence is measured using relative en-tropy. We shall also consider flocking in an incompressiblefluid governed by the Navier-Stokes equations. (Collabo-rators: Jose A. Carrillo, Young-Pil Choi, Antoine Mellet,and Konstantina Trivisa)

Trygve K. KarperNorwegian University of Science and [email protected]

MS24

A Tale of Two Distributions: from Few to ManyVortices In Quasi-Two-Dimensional Bose-EinsteinCondensates

Motivated by the recent successes of particle models in cap-turing the precession and interactions of vortex structuresin quasi-two-dimensional Bose-Einstein condensates, we re-visit the relevant systems of ordinary differential equations.We consider the number of vortices as a parameter and ex-plore the prototypical configurations (“ground states’) thatarise in the case of few or many vortices. In the case of fewvortices, we modify the classical result of Havelock [Phil.Mag. 11, 617 (1931)] illustrating that vortex polygons inthe form of a ring are unstable for N ≥ 7. Addition-ally, we reconcile this modification with the recent iden-tification of symmetry breaking bifurcations for the casesof N = 2, . . . , 5. We then examine the opposite limit oflarge N and illustrate how a coarse-graining, continuumapproach enables the accurate identification of the radialdistribution of vortices in that limit.

Theodore KolokolnikovDept. of Mathematics and StatisticsDalhousie [email protected]


Ricardo [email protected]

MS25

A Riemann-Hilbert Approach for the Degasperis-Procesi and Ostrovsky-Vakhnenko Equations

I will present an inverse scattering transform approach,

based on Riemann-Hilbert problems, for the Degasperis-Procesi and Ostrovsky-Vakhnenko equations on the line.The formulation of the initial value problem in terms ofassociated (3×3) matrix Riemann-Hilbert problems allowsus to get the principal term of the long time asymptotics ofits solution, and also to find soliton solutions. Work withD. Shepelsky.

Anne Boutet de MonvelUniversite’ Paris [email protected]

MS25

The Unified Transform and the Riemann-HilbertFormalism

The Unified Transform provides a novel method foranalysing boundary value problems for linear and for in-tegrable nonlinear PDEs. The relationship of this methodwith the Riemann-Hilbert formalism for both scalar andmatrix problems will be elucidated.

Athanassios S. FokasUniversity of [email protected]

MS25

Long-Time Asymptotics for the Toda Shock Prob-lem

Consider the doubly infinite Toda lattice with steplike ini-tial data and non-overlapping background spectra. We ap-ply the method of nonlinear steepest descent to computethe leading term of the long-time asymptotics of the Todashock problem in all principal regions of the space-time halfplane under the assumption that no discrete spectrum ispresent.

Johanna Michor, Gerald TeschlUniversity of Wien (Austria)[email protected], [email protected]

Iryna EgorovaILTPE [email protected]

MS25

A Coupling Problem for Entire Functions and ItsApplication to the Long-Time Asymptotics of In-tegrable Wave Equations

We propose a novel technique for analyzing the long-time asymptotics of integrable wave equations in the casewhere the underlying isospectral problem has purely dis-crete spectrum. To this end we introduce a natural cou-pling problem for entire functions which serves as a re-placement for the usual Riemann-Hilbert approach, whichdoes not work for these kind of problems. As a prototyp-ical example we investigate the long-time asymptotics ofthe dispersionless Camassa-Holm equation improving thecurrently known results.

Gerald TeschlUniversity of Wien (Austria)[email protected]

Jonathan Eckhardt

88 NW14 Abstracts

Cardiff [email protected]

MS26

Effective Boundary Conditions: An Application tothe Atmosphere

In this talk we present an application of the theory inthe previous talk to the dry atmosphere. While the at-mosphere does not have a definite top, it can be modeledas finite because the buoyancy frequency has a jump at thetropopause. This, effectively, acts as a “leaky” lid on thelower atmosphere. The leakage of gravity waves from thetroposphere to the stratosphere is a significant physical ef-fect that cannot be ignored — as happens when a rigid lidis added at the tropopause. In this talk we show how todevelop effective boundary conditions at the tropopause,using the theory in the previous talk and transform meth-ods.

Lyubov ChumakovaUniversity of [email protected]


Esteban G. TabakCourant InstituteNew York [email protected]

MS26

Particle Trajectories Beneath Stokes’ Waves

We study particle trajectories beneath a Stokes’ wave inthe following regimes: (a) in the presence of a current, (b)in the presence of a submerged structure, and (c) in thepresence of constant vorticity, where the particle phase-space and related pressure distribution are described indetail.

Paul A. MilewskiDept. of Mathematical SciencesUniversity of [email protected]

Andre NachbinIMPA, Rio, [email protected]

Roberto Ribeiro-JuniorIMPA, [email protected]

MS26

Effective Boundary Conditions for Semi-Open Dis-persive Systems

In the classical linear dispersive wave theory it is shownthat sinusoidal waves (i.e., ∝ ei(kx−ωt)) carry energy withthe group speed cg = dω/dk. This concept is limited to thecase where both the frequency ω(k) and the wavenumberk must be real. On the other hand, semi-open dispersivesystems allow more than just sinusoidal solutions: they can

have exponentially blowing up and/or decaying solutions aswell. In these cases the concept of an energy propagationspeed looses meaning, but direction of propagation doesnot. Equations to determine the direction of propagationcan then be implemented by considering the flux of energy.In this first talk (out of two) we show how this can beimplemented to develop radiation boundary conditions forsemi-open dispersive systems. We also show that there isa connection between this concept and the branch cuts ofthe dispersion relation in the complex plane.


Lyubov ChumakovaUniversity of [email protected]


MS26

Diapycnal Mixing and Overturning Circulations

This talk explores a framework to quantify the large-scaleeffects of fluid mixing without resolving the associatedsmall scale motion. The equations of motion for hydro-static flows adopt the form of a hyperbolic system of non-linear equations, which typically yield breaking waves. Inorder to model the shock waves that ensue, one needs toinvolve integral conserved quantities, such as mass and mo-mentum. Yet in a system composed of layers that maymix, first physical principles do not provide a set of con-served quantities large enough to completely determine theflow. Our proposal is to replace the conventional conser-vations laws of each layer’s mass and momentum, invalidafter shocks form, by others, such as energy, in a way thatprovides a natural description of the mixing process. Thisclosure is then applied to modeling overturning circula-tions, such as the Hadley cells of tropical convection.


MS27

Solitary Wave Dynamics in Plasmonic Binary Ar-rays

Novel photonic devices provide the possibility of beingmore efficient, smaller and richer in their functionality. Atthe same time they are an excellent platform in the ongo-ing general study of nonlinear light propagation dynamics.Our work represents efforts in the study of photonic binarysystems that are discrete in nature. Results will be pre-sented on the existence and properties of localized modesand on the natural extension of the model to a continuumapproximation leading to systems of coupled PDEs. this isa joint effort with Prof. C. De Angelis, Drs. A. Auditoreand M. Conforti from U. Brescia in Italy


NW14 Abstracts 89

Costantino De AngelisUniversity of Brescia, Brescia, [email protected]

Aldo AuditoreUniversity of [email protected]

Matteo ConfortiUniversita di Brescia, [email protected]

MS27

Stochasticity and Coherent Structures in Ultra-Long Mode-Locked Lasers

Ultra-long mode-locked lasers are known to be stronglyinfluenced by nonlinear interactions in long cavities thatresults in noise-like stochastic pulses. Here, by using an ad-vanced technique of real-time measurements of both tem-poral and spatial (over round-trips) intensity evolution, wereveal an existence of wide range of generation regimes.Different kinds of coherent structures including dark andgrey solitons and rogue-like bright coherent structures areobserved as well as interaction between them are revealed.

Dmitry ChurkinAston [email protected]

MS27

Movement of Gap Solitons across Deep Gratings inthe Periodic NLS

Moving pulses in nonlinear periodic media can be applied,e.g., as information carriers in photonic crystals. We con-sider the 1D periodic nonlinear Schroedinger equation asa prototype model. For asymptotically small contrasts ofthe periodic structure the equation has moving pulses ap-proximated by gap solitons of the coupled mode equations[Aceves, Wabnitz, Phys. Lett. A, 1989]. These gap solitonshave a wide range of velocities v ∈ (−cg, cg). We show thatanalogous moving pulses exist also in large contrast struc-tures described by perturbed finite band potentials due tothe opening of spectral gaps from a transversal intersectionof band functions.

Tomas DohnalTU DortmundDepartment of [email protected]

MS27

Periodic and Relative Periodic Solutions in a Mul-tiple Waveguide System

We describe the propagation of light in multi-waveguidesystems modeled by the nonlinear Schrodinger and discretenonlinear Schrodinger equations using normal form meth-ods and other ideas from Hamiltonian systems. We reporton new families of relative periodic orbits that coexist withthe familiar nonlinear normal modes in these systems.

Roy GoodmanNew Jersey Institute of Technology

[email protected]

MS28

Azimuthal Dissipative Structures in Whispering-Gallery Mode Resonators

Different regimes of Kerr optical frequency combs can begenerated in ultra-high Q resonators pumped by a contin-uous wave laser. We use a 1-dimension Lugiato-Lefeverequation to theoretically describe their dynamics. In par-ticular, we show that these combs correspond to differentspatio-temporal structures such as Turing patterns, brightand dark solitons. We discuss the parameter ranges for thegeneration of such combs, and relate them to our experi-mental results obtained in crystalline resonators.

Aurelien CoilletOptics departmentFEMTO-ST Institute, Besancon, [email protected]

MS28

Injection Locking of Frequency Combs in ModeLocked Lasers

Injection locking of mode locked laser to an external pulsetrain entails the entrainment of two frequencies, the pulseto pulse timing and overall phase shift, synchronizing thesource and target frequency combs. For a given injec-tion strength, we demonstrate the domain of stable syn-chronization in the plane of comb spacing and offset mis-matches. The shape of the synchronization domain de-pends on the pulse shape and chirp, and it is bounded by aline of saddle-node and higher co-dimension bifurcations.

Omri GatHebrew University of Jerusalem, Department of PhysicsJeruslam, [email protected]

David KielpinskiAustralian Attosecond Science FacilityGriffith University, Brisbane, [email protected]

MS28

Dynamics of Frequency Comb Generation and De-sign of Planar Microring Resonators

We study the generation of optical frequency combs frommicroresonators and show that a truncated dynamicalmodel can capture the essential nonlinear dynamics of bothstable and chaotic patterns. We also present an analyticalapproach for obtaining linear and nonlinear design param-eters of planar microring resonators. Closed form approxi-mations for the eigenmode/eigenfrequency problem are de-rived for resonators possessing a large radius to width ratioand examples are presented for silicon microrings.

Tobias Hansson, Daniele Modotto, Stefan WabnitzUniversity of [email protected],[email protected], ste-

90 NW14 Abstracts

[email protected]

MS28

Tunable Photonic Oscillators

Limit cycle oscillators are used to model a broad range ofperiodic nonlinear phenomena. Using the optically injectedsemiconductor oscillator as key Paradigm architecture wewill demonstrate that at specific islands in the optical de-tuning and injection level map, the Period one limit fre-quency is simultaneously insensitive to multiple perturba-tion sources. In our system these include the temperaturefluctuations experienced by the master and slave lasers aswell as fluctuations in the bias current applied to the slavelaser. Tuning of the oscillation frequency then dependsonly on the injected optical field amplitude. Experimen-tal measurements are in good quantitative agreement withnumerical modeling and analysis based on reduced gener-alized Adler phase equations. These special operating re-gions should prove valuable for developing ultrastable non-linear oscillators, such as sharp linewidth, frequency tun-able photonic microwave oscillators. Finally the concept ofan Isochron originally developed in mathematical biologywill be reviewed and placed on context for efficient design ofstable frequency sources via systems of coupled limit cyclesoscillators. Time permitting a few new theoretical resultson injecting monothematic signals into quantum cascadelaser gain media will be outlined.

Vassilios KovanisBradley Department of Electrical and ComputerEngineeringVirginia [email protected]

MS29

Transverse Dynamics of Periodic Gravity-CapillaryWater Waves

We study the transverse dynamics of two-dimensionalgravity-capillary periodic water waves in the case of crit-ical surface tension. We show that, as solutions of thefull water-wave equations, the periodic traveling wavesare linearly unstable under three-dimensional perturba-tions which are periodic in the direction transverse to thedirection of propagation. Then we discuss the nonlinearbifurcation problem near these transversely unstable two-dimensional periodic waves. We show that a one-parameterfamily of three-dimensional doubly periodic waves is gen-erated in a dimension-breaking bifurcation.

Mariana HaragusUniversite de [email protected]

Erik WahlenLund [email protected]

MS29

Stability of Viscous Roll-Waves

Roll-waves are a well observed hydrodynamic instabilityoccurring in inclined thin film flow, mathematically de-scribed as periodic traveling wave solutions of the St.Venant system. In this talk, I will discuss recent progressconcerning the stability of viscous roll-waves in a variety

of asymptotic regimes, including near the onset of hydro-dynamic instability and in the inviscid limit. Our analysisrelies on Evans function calculations, geometric singularperturbation theory, Whitham theory, and spectral per-turbation theory.

Mat JohnsonUniversity of [email protected]

Pascal NobleUniversity of [email protected]

Miguel RodriguesUniversity of [email protected]

Kevin ZumbrunIndiana [email protected]

Blake BarkerIndiana [email protected]

MS29

Stability of Traveling Waves on Vortex Filaments

We develop a framework for studying the linear stabilitysolutions of the Vortex Filament Equation (VFE), basedon the correspondence between the VFE and the NLS pro-vided by the Hasimoto map. This framework is applied tovortex filaments associated with periodic NLS solutions.We focus on a class of torus knots VFE solutions and showthat they are stable only in the unknotted case. We alsoestablish the spectral stability of soliton solutions.

Stephane Lafortune, Annalisa M. CaliniCollege of CharlestonDepartment of [email protected], [email protected]

Scotty KeithCollege of [email protected]

MS29

Orbital Stability of Periodic Waves and Black Soli-tons in the Cubic Defocusing NLS Equation

Standing periodic waves of the cubic defocusing NLS equa-tion are considered. Using tools from integrability of thecubic NLS equation, these waves have been shown to belinearly stable by computing the Floquet–Bloch spectrumexplicitly. We combine the first four conserved quantitiesof the cubic NLS equation to give a direct proof that thewaves are also orbitally stable with respect to the subhar-monic periodic perturbations in theH2

per topology. We alsodevelop a new proof of the orbital stability of the black soli-tons in H2(R). This is a joint work with Thierry Gallay(University of Grenoble).

Dmitry PelinovskyMcMaster UniversityDepartment of Mathematics

NW14 Abstracts 91

[email protected]

MS30

Shear-induced Instability of a Smectic A LiquidCrystal

A smectic A liquid crystal is usually described as be-ing composed of rod-like molecules arranged in reasonablywell-defined equidistance layers. Recent models describingthe microscopic organisation of smectic A allow the aver-age molecular orientation to evolve away from the layernormal direction, see for example I.W. Stewart, Contin.Mech. Thermodyn. 18:343-360 (2007). In this presenta-tion we will summarise this continuum theory and apply itto investigate the undulation instability of the smectic Aphase in the presence of an imposed linear shear flow.

Jonathan DawesUniversity of [email protected]

Iain W. StewartUniversity of [email protected]

MS30

Imry-Ma-Larkin Clusters in Random Nematics


Samo KraljFaculty of Natural Sciences and MathematicsUniversity of [email protected]

MS30

Harnessing Topological Defects via Liquid CrystalMicrofluidics

Harnessing interactions between flow, and molecular order-ing in complex anisotropic fluids like liquid crystals pro-vides a novel pathway to engineer flow and topology tem-plates. The interactions emerge due the anisotropic cou-pling between flow and molecular orientation. In microflu-idic parlance, the nature of surface anchoring, channel as-pect ratios, and strength of the flow provide a rich assort-ment of accessible experimental parameters. The emergingfield of Topological Microfluidics promises physics and po-tential applications beyond the conventional isotropic case.

Anupam SenguptaMax Planck Institute for Dynamics and Self-OrganizationGottingen, [email protected]

Stephan HerminghausMax Planck Institute for Dynamics and [email protected]

Christian BahrMax Planck Institute for Dynamics and Self-OrganizationGottingen, Germany

[email protected]

MS30

Frustrated Nematic Order in Spherical Geometries


Vincenzo VitelliAssociate Professor,Soft Condensed Matter Theory GroupInstituut-Lorentz, Universiteit [email protected]

MS31

Thermal Counterflow in a Periodic Channel withSolid Boundaries

We perform numerical simulations of finite temperaturequantum turbulence produced through thermal counter-flow in superfluid 4He, using the vortex filament model.We investigate the effects of solid boundaries along one ofthe cartesian directions, whilst assuming a laminar nor-mal fluid with a Poiseuille profile, whilst varying the tem-perature and the normal fluid velocity. We analyze thedistribution of quantized vortices as a function of the wall-normal direction and find that the vortex line density isconcentrated close to the solid boundaries. Furthermore,we find that the vortex line density profile is independentof the counterflow velocity, and offer an explanation as towhy the peak of vortex line density tends towards the solidboundaries with increasing mutual friction. Finally we of-fer evidence that upon the transition to a turbulent normalfluid, there is a dramatic increase in the homogeneity of thetangle, which could be used as an indirect measure of thetransition to turbulence in the normal fluid component inexperiments.

Andrew BaggaleyUniversity of [email protected]

Jason LaurieWeizmann Institute of [email protected]

MS31

Vortex Reconnections and Implications for InverseEnergy Transfer in Turbulent Superfluid Helium

In superfluid helium vorticity takes the form of discretevortex filaments of fixed circulation and atomic thickness.We present numerical evidence of three-dimensional inverseenergy transfer from small length scales to large lengthscales in turbulence generated by a flow of vortex rings. Weargue that the effect arises from the anisotropy of the flow,which favors vortex reconnections of vortex loops of thesame polarity, and that it has been indirectly observed inthe laboratory. The effect opens questions about analogieswith related processes in ordinary turbulence.

Carlo F. BarenghiApplied Mathematics GroupNewcastle [email protected]

Andrew BaggaleyUniversity of [email protected]

92 NW14 Abstracts

Yuri SergeevNewcastle [email protected]

MS31

Breathers on Quantized Superfluid Vortices

We consider the propagation of breathers along quantisedsuperfluid vortices. Using the correspondence between thelocal induction approximation (LIA) and the nonlinearSchrodinger equation, we identify a set of initial condi-tions corresponding to breather solutions of vortex motiongoverned by the LIA. These initial conditions, which giverise to a long-wavelength modulational instability, resultin the emergence of large amplitude perturbations that arelocalised in both space and time. The emergent structureson the vortex filament are analogous to loop solitons. Al-though the breather solutions we study are exact solutionsof the LIA equations, we demonstrate through full numer-ical simulations that their key emergent attributes carryover to vortex dynamics governed by the Biot-Savart lawand to quantized vortices described by the Gross-Pitaevskiiequation. In these cases, the breather excitations either de-cay or in some cases can lead to self-reconnections, a mech-anism that can play an important role within the cross-overrange of scales in superfluid turbulence. Moreover, the ob-servation of breather solutions on vortices in a field modelsuggests that these solutions are expected to arise in a widerange of other physical contexts from classical vortices tocosmological strings.

Hayder SalmanUniversity of East [email protected]

MS31

Local and Nonlocal Effects in Quantum Turbulence

Quantum turbulence consists of an apparently random tan-gle of quantised vortex lines which move under the influ-ence of each others’ velocity field. We ask the naturalquestion of the relative importance of local and nonlocaleffects on the turbulent velocity at a point, which is de-termined by the instantaneous distribution of vorticity viathe Biot-Savart law. The answer is related to the existenceof (or the lack of) coherent vortex structures in the tur-bulence tangle: the more random the vortex lines are, themore cancellation of far-field effects there will be. We shallpresent numerical results which address and answer thisquestion.

Lucy SherwinNewcastle [email protected]

MS31

Reconnections of Vortex Rings in Superfluid He-lium

Quantized vortex rings in superfluid helium provide anideal model system for investigating the interactions andcollisions occurring within a cloud of unidirectional vortexrings with almost identical radii. We present evidence forsmall vortex rings emitted upon vortex reconnections insuperfluid 4He at very low temperatures. In one exper-iment, pairs of charged vortex rings collided resulting increation of both smaller and larger vortex rings, highlight-ing how energy can be redistributed to both smaller and

larger length scales. In a second experiment, small vortexrings with large mean free path were frequently generatedwhen much larger vortex rings are injected into vortex tan-gles of known density. This only occurred at temperaturesbelow 0.7 K where small wavelength Kelvin waves occurdue to the lack of damping provided by mutual friction.All our observations can be explained using simple modelsbased on vortex reconnections and self-reconnections andprovide new insight into the quantum regime of superfluidturbulence.

Paul Walmsley, P.M. Tompsett, D.E. Zmeev, A.I. GolovUniversity of [email protected],[email protected],[email protected], [email protected]

MS32

A Spectral Approach to Dbar Problems

We present a fully spectral approach to the numerical solu-tion of dbar problems for smooth rapidly decreasing initialdata. As an example we will discuss the Davey-Stewartsonequations.

Christian KleinInstitut de Mathematiques de Bourgogne9 avenue Alain Savary, BP 47870 21078 DIJON [email protected]

MS32

The Semiclassical Sine-Gordon and Rational Solu-tions of Painleve-II

We formulate and study a class of initial-value problemfor the sine-Gordon equation in the semiclassical limit.The initial data parametrizes a curve in the phase por-trait of the simple pendulum, and near points where thecurve crosses the separatrix a double-scaling limit reveals auniversal wave pattern constructed of superluminal kinkslocated in the space-time along the real graphs of all of therational solutions of the inhomogeneous Painleve-II equa-tion. The kinks collide at the real poles, and there the solu-tion is locally described in terms of certain double-kink ex-act solutions of sine-Gordon. This study naturally leads tothe question of the large-degree asymptotics of the rationalsolutions of Painleve-II themselves. In the time remainingwe will describe recent results in this direction, includinga formula for the boundary of the pole-free region, strongasymptotics valid also near poles, a weak limit formula,and planar and linear densities of complex and real poles.This is joint work with Robert Buckingham (Cincinnati).

Peter D. MillerUniversity of Michigan, Ann [email protected]

MS32

Numerical Inverse Scattering for the BenjaminOnoEquation

We investigate the numerical implementation of the for-ward and inverse scattering transform for the Ben-jaminOno equation. Unlike previous numerical inversescattering problems, the transform involves a nonlocalspectral problem, requiring new numerical techniques tobe developed. Joint work with Peter Miller and Tom Trog-

NW14 Abstracts 93

don.

Sheehan OlverThe University of [email protected]

MS32

Oscillatory Integrals and Integrable Systems

High oscillation is an important conservative phenomenonin the theory of integrable systems. For integrable PDEs,two competing forces are in balance. First, the flow regu-larizes and prevents the formation of discontinuities. Sec-ond, an infinite number of quantities are conserved. Inthe necessary absence of dissipation, oscillations must beresponsible for regularization. These oscillations are seento be a direct consequence of oscillatory Fourier symbols.Furthermore, properties of these symbols are used for de-tailed asymptotic and numerical studies of many problems.In this talk, I will discuss recent asymptotic and numericalprogress on integrable PDEs that exploits the structure ofoscillatory integrals.

Thomas TrogdonCourant [email protected]

MS33

The Effect of Rotation on Shoaling Internal Soli-tary Waves

In the weakly nonlinear long wave regime, internal oceanicsolitary waves are often modeled by the Korteweg-de Vriesequation, which is well-known to support solitary waves.However, when the effect of background rotation is takeninto account, the resulting relevant nonlinear wave equa-tion is the Ostrovsky equation, which does not support anexact solitary wave solution. Instead an initial solitary-likedisturbance decays into radiating oscillatory waves withthe long-time outcome being the generation of a nonlinearwave packet, whose carrier wavenumber is determined byan extremum in the group velocity. When variable bottomtopography is also taken into account, although this pro-cess may still take place, some new features emerge suchas the formation of secondary undular bores.

Roger GrimshawUniversity of Loughborough, [email protected]

MS33

Breaking of Interfacial Waves Induced by Back-ground Rotation

The amplitudes of vertical modes in weakly-nonlinear,weakly rotating, horizontally-extended stratified flows aregoverned by the reduced Ostrovsky (RO) equation wheredispersion arises from a non-local integral term. This equa-tion is integrable provided a certain curvature constraintis satisfied. We demonstrate, through theoretical analysisand numerical simulations, that when this curvature con-straint is not satisfied at the initial time, then wave break-ing inevitably occurs. Similar results are obtained for themodified (cubic) RO.

Ted JohnsonUCLLondon, UK

[email protected]

MS33

Pure Gravity Generalised Solitary Waves

Steep waves travelling at a constant velocity at the surfaceof an incompressible and inviscid fluid of infinite depth areconsidered. The flow is assumed to be irrotational andgravity is taken into account. The effect of surface tensionis neglected. It is shown that in addition to the classicalperiodic Stokes waves, there are also non periodic waves.These waves are generalised solitary waves in the sense thatthey are characterised by a periodic train of waves in thefar field. Numerical evidence for the existence of new typesof periodic waves is also presented.

Jean-Marc Vanden-BroeckUniversity College [email protected]

MS34

On the Existence of Breathers in Periodic Media:An Approach Via Inverse Spectral Theory

Breathers are considered a rare phenomenon for constantcoefficient nonlinear wave equations. Recently, a nonlin-ear wave equation with spatially periodic step potentialshas been found to support breathers by using a combina-tion of spatial dynamics, center manifold reduction and bi-furcation theory. Via inverse spectral theory for weightedSturm-Liouville equations, we characterize a surprisinglylarge class of potentials that allow breathers. The researchis motivated by the quest of using photonic crystals as op-tical storage.

Martina Chirilus-BrucknerUniversity of [email protected]

C. E. WayneBoston [email protected]

MS34

Reflection of an Incoming NLS Soliton by an At-tractive Delta Potential

We consider the dynamics of a single soliton launched fromspatial infinity with velocity v toward a delta-potentialdefect, evolving according to the 1D cubic NLS equationi∂tu+

12∂2xu+ |u|2u− qδu = 0, where q ∈ R is the coupling

constant and δ is the delta function at x = 0. The case of|q| ∼ |v| � 1 was previously studied and quantum split-ting of the incoming soliton was observed and quantified.In the case of |q| � 1, the soliton was shown to remainintact and obey classical motion. In this paper, we studythe case of intermediate interaction strength |q| ∼ 1, andslow incoming velocity |v| � 1. We show that this is nei-ther a classical nor quantum regime – a small eigenstateemerges on top of the delta potential with phase structureincompatible with the incoming soliton, resulting in reflec-tion of the incoming soliton. Interestingly, this occurs evenfor attractive potentials q ∼ −1.

Justin HolmerDepartment of Mathematics, Brown University,Box 1917, 151 Thayer Street, Providence, RI 02912, [email protected]

94 NW14 Abstracts

Quanhui LinBrown [email protected]

MS34

Analysis of Dispersion Managed Solitary Waves

We study pulses in optical glass fiber cables which havea periodically varying dispersion along the cable. This so-called dispersion management leads to interesting effects inthose cables. Mathematically, these pulses are described bya non-local version of the non-linear Schrodinger equationwhich was derived first by Gabitov and Turitsyn (1996),and and later by Ablowitz and Biondini (1998). The non-local nature of the non-linearity makes the rigorous analysishard. In the talk, we will focus on existence of solitarypulses in these cables and show that they are very well-localized.

Dirk HundertmarkKarlsruhe Institute of [email protected]

MS34

Ground States of a Nonlinear Curl-Curl Problem

In this talk I will report on recent joint work with ThomasBartsch, Tomas Dohnal and Michael Plum. We are inter-ested in ground states for the nonlinear curl-curl equation

∇×∇×U+V (x)U = Γ(x)|U |p−1U in IR3, U : IR3 → IR3.

A basic requirement is to find scenarios, where 0 does notbelong to the spectrum of the operator

L = ∇×∇×+V (x).

Under suitable assumptions on V,Γ we construct groundstates both for the defocusing case (Γ ≤ 0) and the focusingcase (Γ ≥ 0). The main tools are variational methods andthe use of symmetries.

Thomas BartschUniversity of [email protected]

Tomas DohnalKIT, Department of [email protected]

Michael PlumKarlsruhe University (KIT)[email protected]

Wolfgang ReichelKIT, Department of [email protected]

MS35

Novel Phenomena in WGM Resonators with Ver-tical Evanescent Coupling to Bus Waveguides

We will report on novel optical phenomena which manifestin a vertically coupled Whispering-gallery resonator and adielectric waveguide. In particular, theoretical predictionsof (a) the oscillatory vertical coupling, characterized bymultiple critical coupling conditions at different gaps, and

(b) the non-diagonal analogue of the Lamb shift for clas-sical photons will be presented. Supporting experimentalobservations of these novel optical phenomena confirm theunique characteristics of the evanescent vertical couplingin an integrated photonic platform.

Mher GhulinyanFondazione Bruno [email protected]

MS35

Terabit Communications Using Optical FrequencyCombs

Terabit/s optical interconnects rely on advancedwavelength-division multiplexing (WDM) schemes,where information is transmitted by a multitude opti-cal channels of different wavelengths. In this context,frequency combs are a particularly attractive optionfor generating the associated optical carriers. In thispaper, we give an overview on our recent demonstrationsof terabit/s communications using optical frequencycombs. Our experiments exploit different comb generationschemes relying, e.g., on electro-optic modulation and onKerr-nonlinear interaction in high-Q microcavities.

Christian KoosKarlsruhe Institute of [email protected]

MS35

Noise of Frequency Combs Based on Yb FiberLasers with Self-Similar Pulse Evolution

Measurements of the free running carrier envelope offsetfrequency linewidth of a similariton based optical frequencycomb show that the frequency noise of the laser is indepen-dent of net cavity dispersion. The experimental results areconsistent with simulations of the quantum-limited tim-ing noise. The resultant possibilities for low-noise, high-performance fiber sources will be discussed.

William [email protected]

MS35

Stability of Modelocked Lasers With Slow Sat-urable Absorbers

Lasers that are modelocked with semiconductor saturableabsorbers are of great practical interest because they can bemore environmentally stable than other modelocked lasers.However, the slow saturable absorber opens a gain windowthat can lead to instability in the wake of modelocked soli-ton pulse. In this paper, we characterize the spectrum ofthis instability and its evolution.

Shaokang [email protected]


MS36

Stability of Solitary Waves in Nonlinear Dirac

NW14 Abstracts 95

Equation

We study the linear instability of solitary wave solutionsφ(x)e−iωt to the nonlinear Dirac equation. That is, welinearize the equation at a solitary wave and examine thepresence of eigenvalues with positive real part. We de-scribe recent analytic and numerical results. In particu-lar, we show that small amplitude solitary waves in theSoler model are linearly unstable in three spatial dimen-sions, but are generically stable in one dimension. We usethe limiting absorption principle and the Carleman-typeestimates of Berthier–Georgescu to locate the part of thecontinuous spectrum of the linearized system, from whichpoint eigenvalues can bifurcate (leading to linear instabil-ity). We also show that the border of the linear instabilityregion is described not only by the Vakhitov-Kolokolov con-dition Q′(ω) = 0, obtained in the NLS context, but alsoby the energy vanishing condition, E(ω) = 0. Here E, Qare the energy and the charge of a solitary wave with fre-quency ω. Some of the results are obtained in collaborationwith Nabile Boussaid, Universite de Franche-Comte, DavidStuart, University of Cambridge, Stephen Gustafson, Uni-versity of British Columbia, Gregory Berkolaiko and AlimSukhtayev, Texas A&M University.

Andrew ComechDepartment of MathematicsTexas A&M [email protected]

MS36

Approximation of Traveling Waves on Finite Inter-vals

Usually, traveling waves are not a meaningfull object forpartial differential equations posed on finite intervals. Butby using the method of freezing, proposed by Beyn andThummler in 2004, one is able to calculate a suitable co-moving frame on the fly so that in this new system a sta-ble traveling wave of the original system becomes a stablestanding wave in the new system. More precisely, in themethod of freezing one rewrites the original problem asa partial differential algebraic equation that includes thevelocity of a suitable co-moving frame as an additional un-known. For this new system it does make sense to restrictto a finite interval. To obtain a well-posed problem, onethen has to impose artificial boundary conditions. We con-sider this procedure in the case of semilinear hyperbolicproblems and show how the new system on a finite inter-val approximates the original problem and can be used innumerical computations.

Jens Rottmann-MatthesUniversity of [email protected]

MS36

Concatenated Traveling Waves

We consider concatenated traveling wave solutions ofreaction-diffusion systems. These are solutions that looklike a sequence of traveling waves with increasing velocity,with the right state of each wave equal to the left state ofthe next. I will present an approach to the stability theoryof such solutions that does not rely on treating them as asum of traveling waves. It is based instead on exponentialdichotomies and Laplace transform.

Stephen Schecter, Xiao-Biao LinNorth Carolina State University

Department of [email protected], [email protected]

MS36

Stability of Traveling Standing Waves for the Klein-Gordon Equation

For the Klein-Gordon equation, the stability of the travel-ing standing waves is considered and the exact ranges ofthe wave speeds and the frequencies needed for stabilityare derived. This is done in both the whole line case andthe periodic case.

Milena StanislavovaUniversity of Kansas, LawrenceDepartment of [email protected]

MS37

Two Component Condensates: Spin Orbit Cou-pling and Defects

Two component condensates emerge from the physics ofartificial gauge potentials and can describe a single isotopein two different hyperfine spin states, two different isotopesof the same atom or isotopes of two different atoms. I willdescribe both numerical and theoretical results concerningspin orbit coupled two component condensates. I will ex-plain how some segregation cases can be analyzed througha Gamma limit leading to a phase separation problem ofde Giorgi type. In the coexistence cases, we try to obtainan asymptotic expansion of the energy taking into accountthe various types of defects. The first term in the expan-sion is related to the Thomas Fermi limit of the profile andrelies on singular perturbation techniques, while the nextones require a more precise analysis of the defects: vortexsheets, vortices or skyrmions

Amandine AftalionUniversity of Paris VI and [email protected]

MS37

Convergence to an Equilibrium for Wave Maps ona Curved Manifold

We consider equivariant wave maps from a wormhole-typespacetime into the three-sphere. This is a toy-model forgaining insight into the dissipation-by-dispersion phenom-ena, in particular the soliton resolution conjecture. Usingthe hyperboloidal formulation of the initial value problem,we show that, for a given topological degree of the map,all solutions starting from smooth initial data converge tothe unique stationary solution as time goes to infinity. Theasymptotics of this relaxation process is described in detail.

Piotr BizonInstitute of PhysicsJagiellonian [email protected]

MS37

A Gradient Flow Approach to the Keller-Segel Sys-tems


Adrien Blanchet

96 NW14 Abstracts

Ceramade, [email protected]

MS37

Vortices and Vortex Lattices in the Ginzburg-Landau and Bcs Theories

The Ginzburg-Landau theory gives a fairly good macro-scopic description of superconductors and the effect of mag-netic fields on them. This theory is based on the Ginzburg-Landau equations, a pair of coupled nonlinear equations forthe macroscopic wave function (order parameter) and mag-netic potential. (These equations appear also in abeleanHiggs model with unknowns called the Higgs and gaugefields and, in general, serve as a paradigm for the descrip-tion of a large class of phenomena in physics, material sci-ence and biology.) In this talk I will review recent rigorousresults on the key solutions of these equations - the mag-netic vortices and magnetic vortex lattices, their existenceand stability. I will also discuss relation of the Ginzburg-Landau theory to the microscopic BCS theories and thedescription of vortices and vortex lattices in the latter.

Israel Michael SigalDepartment of MathematicsUniversity of [email protected]

MS38

Stability of Periodic Traveling Waves for NonlocalDispersive PDE

We discuss recent work on the stability of periodic travel-ing wave solutions to nonlinear PDE of KdV-type, allow-ing for nonlocal phase speeds. Specific examples includefractional KdV with phase speed |ξ|α for some α > 1/2,and Whitham’s water wave equation with the exact (uni-directional) phase speed from the Euler equations. Wedemonstrate the existence of an explicit stability index,computable entirely from the linear phase speed, whichdetermines the modulational stability of small amplitudewaves.

Mat JohnsonUniversity of [email protected]

Vera HurUniversity of Illinois at [email protected]

MS38

Dispersive Perturbations of Burgers and Hyper-bolic Equations

The aim of this talk is to show how a weakly dispersiveperturbation of the inviscid Burgers equation improve (en-large) the space of resolution of the local Cauchy problem.We will also review several problems arising from weak dis-persive perturbations of nonlinear hyperbolic equations orsystems.

Felipe LinaresInstitute of Pure and Applied [email protected]

Didier Pilod

UFRJ, Rio de [email protected]

Jean-Claude [email protected]

MS38

Local Well-posedness for a Class of Nonlocal Evo-lution Equations of Whitham Type

For a class of pseudodifferential evolution equations of theform

ut + (n(u) + Lu)x = 0,

we prove local well-posedness for initial data in the Sobolevspace Hs, s > 3/2. Here L is a linear Fourier multi-plier with a real, even and bounded symbol m, and n isa real measurable function with n′′ ∈ Hs

loc(R), s > 3/2.The proof, which combines Kato’s approach to quasilinearequations with recent results for Nemytskii operators ongeneral function spaces, applies equally well to the Cauchyproblem on the line, and to the initial-value problem withperiodic boundary conditions.

Long PeiDepartment of Mathematical SciencesNTNU, Trondheim, [email protected]

MS38

Three-Dimensional Solitary Water Waves withWeak Surface Tension

I will discuss a variational existence theory for three-dimensional fully localised solitary water waves with weaksurface tension. The water is modelled as a perfect fluid offinite depth, undergoing irrotational flow. The surface ten-sion is assumed to be weak in the sense that 0 < β < 1/3,where β is the Bond number. A fully localised solitarywave is a travelling wave which decays to the undisturbedstate of the water in every horizontal direction. Such so-lutions are constructed by minimising a certain nonlocalfunctional on its natural constraint. A key ingredient is avariational reduction method, which reduces the problemto a perturbation of the Davey-Stewartson equation.

Boris [email protected]

Mark D. GrovesUniversitat des [email protected]


MS39

Anatomy Induced Drift of Spiral Waves in HumanAtrium

In biophysically and anatomically realistic model of humanatrium, we demonstrate functional effects of atrial anatom-ical structures on spiral waves spontaneous drift. Spiral

NW14 Abstracts 97

waves drift from thicker to thinner regions, along ridge-likestructures of pectinate muscules (PM) and cristae termi-nalis, anchor to PM-atrial wall junctions or to some lo-cations with no obvious anatomical features. The insightcan be used to improve low-voltage de-fibrillation proto-cols, and predict atrial arrhythmia evolution given a pa-tient specific atrial anatomy.

Irina BiktashevaUniversity of [email protected]

Sanjay R. KharcheUniversity of [email protected]

Gunnar SeemannKarlsruhe Institute of [email protected]

Henggui ZhangUniversity of [email protected]

Vadim N. BiktashevCollege of Engineering, Mathematics and PhysicalSciencesUniversity of [email protected]

MS39

Exact Coherent Structures and Dynamics of Car-diac Tissue

High dimensional spatiotemporal chaos underpins the dy-namics associated with life threatening cardiac arrhyth-mias. Our research seeks to suppress these arrhythmiasand restore normal heart rhythms by using low-energytransfers between unstable solutions underlying the chaoticdynamics of cardiac tissue. We describe the search for un-stable solutions of nonlinear reaction diffusion models ofcardiac tissue and discuss recent efforts to understand lo-cal symmetries in terms of pairwise interactions betweenspiral cores.

Greg A. Byrne, Chris MarcotteGeorgia Institute of [email protected],[email protected]

Roman GrigorievGeorgia Institute of TechnologyCenter for Nonlinear Science & School of [email protected]

MS39

Optogenetic Control of Cardiac Electrical Activity:Experimental Insights

Optogenetics, in the broader sense, refers to the use ofgenetically-encoded molecules serving as optical actuatorsor optical sensors for the active interrogation and imagingof biological processes and systems with high specificityand high spatiotemporal resolution. We will report theapplication of these genetic tools to cardiac tissue and willdemonstrate all-optical remote actuation and sensing to

study wave propagation and termination by light.

Emilia EntchevaStony Brook [email protected]

MS39

Spatiotemporal Dynamics of Obstacle-Induced Spi-ral Wave Initiation

Inexcitable obstacles in the heart can act as substratesfor the initiation of spiral waves. We introduced obsta-cles of varying sizes (1-8 mm) into cardiac monolayers withside pacemakers, demonstrating that smaller obstacles (<5mm) are correlated with spiral wave generation. Using acomputational model of the experiments, we showed thatthe location of the obstacle sensitively governed the spa-tiotemporal dynamics of the initiated spiral waves.

Thomas D. QuailMcGill [email protected]

MS40

Large-degree Asymptotics of Generalised HermitePolynomials and Poles of Rational Painleve-IVFunctions

The Painleve-IV equation admits a family of rational so-lutions, indexed by two integers, that can be expressedin terms of certain generalised Hermite polynomials. Inthe large-degree limit the zeros of these polynomials formremarkable patterns in the complex plane resembling rect-angles with arbitrary aspect ratios depending on how theindexing integers grow. Using Riemann-Hilbert analysis wecompute the large-degree asymptotic behavior of the gen-eralised Hermite polynomials and analytically determinethe boundary of the elliptic (i.e. zero/pole) region for theassociated rational Painleve-IV functions. We also obtainasymptotic behavior in terms of Painleve-I functions at thecorners of the elliptic region.

Robert BuckinghamUniversity of [email protected]

MS40

Inverse Scattering Transform for the DefocusingNonlinear Schrodinger Equation with AsymmetricNonzero Boundary Conditions

We develop the inverse scattering transform (IST) forthe defocusing nonlinear Schrodinger (NLS) equation withasymmetric nonzero boundary conditions q(x, 0) → q± asx→ ±∞, where |q−| �= |q+|. The direct problem is formu-lated without using a uniformization variable, taking intoaccount the square root discontinuities of the eigenvalues ofthe asymptotic scattering problems. The inverse problemis formulated in terms of a discontinuous Riemann-Hilbertproblem (RHP).


Emily FagerstromState University of New York at [email protected]

98 NW14 Abstracts

Barbara PrinariUniversity of Colorado, Colorado SpringsUniversity of Salento, Lecce (Italy)[email protected]

MS40

On the Scattering Matrix for AKNS Systems withMatrix-Valued Potentials

We discuss spectral properties and analytic properties ofthe scattering matrix associated with matrix AKNS sys-tems under suitable assumptions on the potentials. Specialattention will be paid to spectral singularities and embed-ded eigenvalues. We present results on the analytic behav-ior of the scattering matrix near such points and study howthe spectrum changes if the system is perturbed.

Martin KlausVirginia [email protected]

MS40

Inverse Scattering Transform for the Focusing NLSEquation with Fully Asymmetric Boundary Condi-tions

We present the inverse scattering transform (IST) for thefocusing nonlinear Schrodinger equation: iqt = qxx+2|q|2q,with non-zero boundary conditions q(x, t) ∼ ql/r(t) =

Al/reiθl/r(t) as x→ ∓∞ in the fully asymmetric case. The

direct problem is shown to be well-posed for NLS solu-tions q(x, t) such that q(x, t) − ql/r(t) ∈ L1,1(R∓) withrespect to x for all t ≥ 0, for which analyticity propertiesof eigenfunctions and scattering data are established. Theinverse scattering problem is formulated both via (left andright) Marchenko integral equations, and as a Riemann-Hilbert problem on a single sheet of the scattering vari-

ables λl/r =√k2 +A2

l/r, where k is the usual complex

scattering parameter in the IST. The time evolution of thescattering coefficients is then derived, showing that, unlikethe case of solutions with the same amplitude as x→ ±∞,here both reflection and transmission coefficients have anontrivial time dependence.

Francesco DemontisDipartimento di Matematica e InformaticaUniversita di Cagliari, [email protected]

Barbara PrinariUniversity of Colorado, Colorado SpringsUniversity of Salento, Lecce (Italy)[email protected]

Cornelis Van der MeeDipartimento di Matematica e InformaticaUniversita di Cagliari, [email protected]

Federica VitaleDipartimento di Matematica e Fisica ”Ennio De Giorgi”Universita’ del Salento, Lecce (Italy)[email protected]

MS41

Tropical-Extratropical Wave Interactions in a

Moist 2-Layer Model

The coupling between moist convective processes and large-scale circulation is at the core of tropical-extratropicalatmospheric interactions, which, in turn, are known tostrongly modulate rainfall at low latitudes. For example,within the tropical Eastern Pacific, observations suggestthat poleward transport of moisture and energy is par-ticularly dependent upon intrusion of large-scale transientRossby waves from the extratropics towards the equator,particularly during northern winter. Theories for the re-lationship between low latitude moist convection and ex-tratropical waves have emphasized the role of upper levelpotential vorticity (PV) intrusions associated with Rossbywave breaking. In this talk, two major drawbacks of thisapproach are discussed: the limitations of PV inversion atlow latitudes and the neglect of latent heating feedbacks.To address these limitations, an alternative reduced modelis proposed that is based on a barotropic-baroclinic shal-low water system coupled to a water vapor equation. Thewater vapor equation is coupled to the dynamical vari-ables through a simple parametrization for precipitation,allowing for a two-way feedback between precipitation andwaves. This model is used to investigate modulations ofequatorial rainfall, in particular, the relative roles of zonalmoisture transport by tropical waves and meridional mois-ture advection by extratropical waves. By integrating themodel using initial conditions consistent with the northernwinter basic state, we demonstrate the key role of advec-tion of moisture towards the equator due to extratropicalRossby waves. The transient response and tropical rainfallsensitivity to precipitation parametrization and extratrop-ical wave amplitude and scales are discussed, as well as themodel predictions overall agreement with observations andmore complex models.

Juliana F. DiasNOAA Earth System Research [email protected]

MS41

Pilot Wave Dynamics in a Rotating Frame: OrbitalQuantization and Multimodal Statistics

We present the results of a theoretical investigation ofdroplets walking on a rotating vibrating fluid bath. Thedroplet’s trajectory is described in terms of an integro-differential equation that incorporates the influence of itspropulsive wave force. Predictions for the dependence ofthe orbital radius on the bath’s rotation rate compare fa-vorably with experimental data and capture the progres-sion from continuous to quantized orbits as the vibrationalacceleration is increased. The orbital quantization is ratio-nalized by assessing the stability of the orbital solutions,and may be understood as resulting directly from the dy-namic constraint imposed on the drop by its monochro-matic guiding wave. The stability analysis also predictsthe existence of wobbling orbital states reported in recentexperiments, and the virtual absence of stable orbits in thelimit of large vibrational forcing. The droplet’s trajectoryis numerically simulated in this limit, revealing a chaoticdynamics whose statistical properties reflect the persistentinfluence of the unstable orbital solutions.

Anand OzaMath. Dept., MIT.

NW14 Abstracts 99

[email protected]

MS41

Nonlinear Wave Interactions in Global Nonhydro-static Models

In previous works we have analyzed the nonlinear wave in-teractions in a shallow global non-hydrostatic model. Herethis analysis has been extended for the case where thefull Coriolis force terms are considered. The full Corilisforce terms include those proportional to 2ΩcosΦw and2ΩcosΦu in the zonal and vertical momentum equations,respectively, which are disregarded in hydrostatic modelsfor energetics consistence. For simplicity we have consid-ered the mid-latitude beta-plane approximation.

Carlos Raupp

IAG/University of Sao [email protected]

Andre TeruyaIAG/University of Sao [email protected]

MS41

The Influence of Fast Waves and Fluctuations onthe Evolution Three Slow Limits of the BoussinesqEquations

We present results from a study of the impact of the non-slow (typically fast) components of a rotating, stratifiedflow on its slow dynamics. In order to understand how theflow approaches and interacts with the slow dynamics wedecompose the full solution, where u is a vector of all theunknowns, as u = uα + u′

αwhere α represents the Ro →0, F r → 0 or the simultaneous limit of both (QG for quasi-geostrophy), with Pαu

α = uα, Pαu′α = 0, and where Pαu

represents the projection of the full solution onto the nullspace of the fast operator. Numerical simulations indicatethat for the geometry considered (triply periodic) and thetype of forcing applied, the fast waves act as a conduit,moving energy onto or off of the slow ’manifold’.

Beth WingateUniversity of [email protected]

Jared WhiteheadBrigham Young [email protected]

Terry HautLos Alamos National [email protected]

MS42

Minimizing the NLS Energy on General Graphs

We treat the problem of finding the ground state for a sys-tem driven by the Nonlinear Schroedinger Equation andevolving on a ramified structure (graph). We prove tworesults: first, if the graph is made of at least two half linesmeeting in an arbitrary compact graph, then there is nonminimizer. Second, if the graph is a star graph with two in-finite edges and a finite one, then there exists a minimizer,

whose shape can be quite explicitly decsribed.

Riccardo AdamiUniversity of [email protected]

Enrico Serra, Paolo TilliPolitecnico di [email protected], [email protected]

MS42

Micro/macroscopic Models for Fluid Flow in Net-works of Elastic Tubes

We describe a Boussinesq-type system for modeling thedynamics of pressure-flow in arterial networks, consideredas a 1d spatial network of elastic tubes. Numerical solu-tions of the system of PDEs are compared with simplifiedmicroscopic models based on particle-tracking arguments,and are used to study flow optimization task, dependingon the geometry and size of the network. Physiologicallyrealistic control mechanisms are tested in the context ofthese simplified models.

Radu C. CascavalUniversity of Colorado at Colorado [email protected]

MS42

Solution Formulas for the Linearized KdV Equa-tion on Graphs

We investigated linearized KdV equation on metric stargraphs with at least three semi-infinite bonds. Under someassumption on the coefficients of the vertex conditionsuniqueness of solution are proven. It is known that theoryof potentials for linearized KdV equation are well studied.Using this theory we reduced the considered problem to theequivalent system of linear algebraic equations. It is shownthat the obtained system of equations is uniquely solvableunder conditions of the uniqueness theorem. By using ofderived formulas for the solutions we proved the existencetheorems in the classes of Schwartz functions decreasing atinfinity and in Sobolev classes.

Zarif A. SobirovTashkent Financial [email protected]

Hannes UeckerDepartment of MathematicsUniversity of [email protected]

Maksad AkhmedovTashkent Financial [email protected]

MS42

The NLS on Fat Graphs and the Metric GraphLimit

The description of the propagation of waves through net-works is often based on metric graphs, consisting of 1Dbonds joined at vertices. However, real waveguides are not1D, and networks are not constructed of 1D bonds con-nected at 0D vertices, but rather the bonds and the vertexregions have a certain thickness ε. These structures are

100 NW14 Abstracts

often refered as “fat graphs’. Here we compare numeri-cal solutions of Nonlinear Schrodinger equations (NLS) onfat graphs with solutions of the formally derived NLS onthe metric graph, in the limit ε → 0. In particular, weshow that an interesting transmission formula for the met-ric graph limit lifts to the fat graph with small errors.

Hannes UeckerDepartment of MathematicsUniversity of [email protected]

Zarif A. SobirovTashkent Financial [email protected]

MS43

One AC and Two PT Nonlinear Schrodinger Dimers

We compare nonlinear dynamics and phase space geome-try of the standard PT -symmetric nonlinear Schrodingerdimer to those of its two modifications. One observation isthat the addition of the nonlinear coupling softens the PT -symmetry breaking transition in the standard dimer: sta-ble periodic and quasiperiodic states persist for any valueof the gain-loss coefficient. Another result is that the in-troduction of active coupling (AC) changes the nonlinearityfrom the promotor to a suppressor of blowup regimes.

Igor BarashenkovUniversity of Cape [email protected]

MS43

Coupled PT-Symmetric Systems

Inspired by recent experiments on a PT-symmetric systemof coupled optical whispering galleries, we study a modelof two coupled oscillators with loss and gain. There aretwo PT transitions: PT symmetry is broken for small andvery large coupling, but unbroken for intermediate cou-pling. The classical and the quantized systems transition atthe same couplings. An oscillating charged particle back-reacting with its own electromagnetic field is also a PT-symmetric system.

Carl M. BenderWashington University in St. [email protected]

MS43

Linear and Nonlinear Properties of PT-symmetricOptical Systems


Demetrios ChristodoulidesCollege of Optics and Photonics/CREOLUniversity of Central [email protected]

MS43

New Aspects of Nonlinear PT-Symmetric Plaque-ttes

Nonlinear Schrodinger equations for PT-symmetric plaque-tte type setups are used as toy models for investigations of

general geometric structures connected with the bifurca-tion dynamics in the vicinity of PT phase transition points.The presentation extends earlier results obtained in collab-oration with Panayotis Kevrekidis, Boris Malomed and KaiLi in (J. Phys. A 45, 444021 (2012)).

Uwe GuentherHelmholtz-Center Dresden-Rossendorf, [email protected]

MS43

Pt-Symmetric Synthetic Materials

In this talk we will introduce a new class of optical struc-tures that rely on the recently developed notion of parity-time (PT) symmetry. These PT synthetic materials can ex-hibit a number of unique characteristics provided that theoptical processes of gain, loss, and index guiding are judi-ciously designed. In particular, we examine the scatteringproperties of PT-symmetric optical Fabry-Perot cavities.Multiple phase transitions and unidirectional invisibilityfor both polarizations are systematically examined.

Konstantinos MakrisSchool of Engineering, Optics LaboratoryEcole Polytechnique Federale de [email protected]

Stefan RotterInstitute for Theoretical PhysicsVienna University of Technology, [email protected]

Demetrios ChristodoulidesCollege of Optics and Photonics/CREOLUniversity of Central [email protected]

MS44

Evans Function Analysis of Viscous Multidimen-sional Shock Layers

We give an overview of our recent work on the stability ofmultidimensional shock layers in multi-dimensional com-pressible fluid flow, in particular the Navier-Stokes equa-tions. Our work involves a careful combination of asymp-totic ODE and Evans function methods. We discuss thesubstantial challenges observed when computing the Evansfunction in Eulerian coordinates at high frequencies. Weshow how to overcome these problems by transforming intocanonical and somewhat general coordinates. The resultsare surprising.

Jeffrey HumpherysBrigham Young [email protected]

Greg LyngDepartment of MathematicsUniversity of [email protected]

Kevin ZumbrunIndiana UniversityUSA

NW14 Abstracts 101

[email protected]

MS44

Computing the Refined Stability Condition forShock Waves

The classical (inviscid) stability analysis of shock waves isbased on the Lopatinskiı determinant, Δ—a function offrequencies whose zeros determine the stability of the un-derlying shock. A careful analysis of Δ shows that in somecases the stable and unstable regions of parameter spaceare separated by an open set of parameters. Zumbrun andSerre [Indiana Univ. Math. J., 48 (1999) 937–992] haveshown that, by taking account of viscous effects not presentin the definition of Δ, it is possible to determine the pre-cise location in the open, neutral set of parameter space atwhich stability is lost. In particular, they show that thetransition to instability under suitably localized perturba-tions is determined by an “effective viscosity’ coefficientgiven in terms of the second derivative of the associatedEvans function, the viscous analogue of Δ. Here, we de-scribe the practical computation of this coefficient.

Gregory LyngDepartment of MathematicsUniversity of [email protected]

MS44

Linear and Spectral Stability of Solitary GravityWaves

The talk will discuss linear and spectral stability of two-dimensional solitary waves on water of finite depth. It isassumed that the fluid is bounded by a free surface and arigid horizontal bottom. The solitary wave is moving un-der the gravity (no surface tension). It was known thatthe fully nonlinear Euler equations have a solitary-wavesolution. In this talk, we will show that the linear opera-tor arising from linearizing the Euler equations around thesolitary-wave solution has no spectrum points lying on theright half of the complex plane, which implies the spectralstability of the solitary waves. Moreover, under the normwith exponential weight, the solitary waves are linearly sta-ble. (This is a joint work with R. Pego)

Shu-Ming SunVirginia TechDepartment of [email protected]

MS44

The Evolution of Traveling Waves in a SimpleIsothermal Chemical System

We study a reaction-diffusion system for an isothermalchemical reaction scheme governed by a quadratic autocat-alytic step and a decay step. Note that this system doesnot enjoy the comparison principle. Previous numericalstudies and experimental evidences demonstrate that if theautocatalyst is introduced locally into this autocatalytic re-action system where the reactant initially distributes uni-formly in the whole space, then a pair of waves will begenerated and will propagate outwards from the initial re-action zone. We will analytically study this phenomena.

Je-Chiang TsaiDepartment of Mathematics

National Chung Cheng University (Taiwan)[email protected]

MS45

Regularity and Stability of Landau-Lifshitz Flows

The Landau-Lifshitz equations of ferromagnetism are ge-ometric PDE for maps into the 2-sphere, which includeas special cases the harmonic map heat flow and theSchroedinger flow. While flows of topological degree 1which form singularities are known, we present resultsshowing that symmetric flows of higher degree, even withlarge energy, remain regular, and flow toward harmonicmaps.

Stephen GustafsonDepartment of MathematicsUniversity of British [email protected]

MS45

Dynamics of Bec of Fermion Pairs in the Low Den-sity Limit of Bcs Theory

We show that the time-evolution of the wave function de-scribing the macroscopic variations of the pair density inBCS theory can be approximated, in the dilute limit, by atime-dependent Gross-Pitaevskii equation. For the staticcase we can as well include direct and exchange energies inorder to obtain a similar result.

Christian HainzlMathematisches InstitutUniversity of [email protected]

MS46

Dissipation and Dispersion in Shallow Water

In a series of physical experiments of surface water waves,dissipation and dispersion appear to play important roles inthe evolution of waves of depression. This suggests that the(conservative, nondispersive) shallow-water wave equationsmiss some important features of the evolution. In this talkwe compare measurements from a series of shallow-waterexperiments with numerical simulations of dispersive anddissipative shallow-water wave models.

John CarterSeattle UniversityMathematics [email protected]

Harvey SegurDept. of Applied MathematicsUniversity of [email protected]

David L. GeorgeU.S. Geological [email protected]

MS46

Stability of Solitary Waves for the Doubly Disper-sive Nonlinear Wave Equation

The general class of nonlocal nonlinear wave equations

102 NW14 Abstracts

utt −Luxx = B(g(u))xx involves two sources of dispersion,characterized by two pseudo-differential operators L andB. Erbay, Erbay and Erkip (2014) established thresholdsfor global existence versus blow-up in the case of power-type nonlinearities. In a recent study of Erbay, Erbay andErkip (submitted), the existence and stability/instabilityproperties of solitary waves for the above class of non-local nonlinear wave equations have been established us-ing the concentration-compactness method of Lions. Inthis talk, we consider the double-dispersion equation withpower-type nonlinearities, which is a member of the aboveclass, and discuss recent analytical and numerical resultson the stability interval of solitary waves.

Husnu Ata ErbayOzyegin University, [email protected]

Saadet ErbayOzyegin [email protected]

Albert ErkipSabanci [email protected]

MS46

Pseudodifferential Operators on a Half-line and theRiemann-Hilbert Problem

Consider the initial-boundary value problem on a half-linefor the evolution equation

∂tu+ F (D)u = f(x, t), t > 0, x > 0,

where F (D) =m1∑1

ck∂kx +

m2∑1

bk∂βkx +

m3∑1

ak |∂x|αk is a linear

combination of the usual derivative ∂x, the Caputo deriva-tive ∂β

x and the module-fractional derivative |∂x|α on half-line, αk, βk ∈ R, k is integer. Here |∂x|α is a module-fractional derivative

|∂x|α u = R1−α+[α]∂[α]+1x u,

where

Rαu =

∫ +∞

0

sign(x− y)u(y)

|x− y|1−αdy

is the modified Riesz potential. The fractional Caputoderivative ∂β

x is defined as

∂βxu = I1−β+[β]∂[β]+1

x u,

where

Iβu =

∫ x

0

u(y)

(x− y)1−βdy

is Riemann-Liouville fractional derivative. We prove theexistence and the uniquness of the solution. We propose anew method to construct solutions to the initial-boundaryvalue problem. These results could be applied to the studyof a wide class of nonlinear nonlocal equations on half-lineby using the techniques of nonlinear analysis. We give someexamples: nonlinear Schrodinger equation, Benjamin-Onoequation, intermediate long wave equation, and nonlinearKlein-Gordon equation.

Elena KaikinaInstituto de MatematicasNational Autonomous University of Mexico

[email protected]

MS46

A Numerical Method for Computing TravelingWaves of Nonlinear Dispersive Equations

We present an automated Python-powered solver for non-linear nonlocal wave equations such as the Whitham equa-tion, KdV, Benjamin-Ono and alike. The solver is basedon the cosine collocation method. A user supplies the pro-gramme with a nonlinear flux, linear dispersion operatorand some parametres. Given that the input satisfies re-quired conditions, a traveling-wave solution is computedand tested with an evolution integrator. Dynamic simula-tion results are provided for the Whitham and square-rootWhitham equations.

Daulet MoldabayevDepartment of MathematicsUniversity of Bergen, [email protected]

MS47

Measuring Scroll Filament Rigidity

Spherical glass beads can pin three-dimensional scrollwaves in the Belousov-Zhabotinsky reaction. Three pin-ning sites cause initially circular scroll filaments to ap-proach equilateral triangles. The resulting stationaryshapes show convex deviations that increase with anchorradii. We describe the shapes of the filament segmentsanalytically using an asymptotic theory, that takes intoaccount filament tension and rigidity. Fitting the theoret-ical shapes to experimental data, with knowledge of fila-ment tension, allows experimental measurement of filamentrigidity.

Vadim N. BiktashevCollege of Engineering, Mathematics and PhysicalSciencesUniversity of [email protected]

Elias Nakouzi, Zulma JimenezFlorida State [email protected] ¡[email protected],[email protected] ¡[email protected]

Oliver SteinbockDepartment of Chemistry and BiochemistryFlorida State [email protected]

MS47

Effective Dynamics of Twisted and Curved ScrollWaves Using Virtual Filaments

Scroll waves are three-dimensional excitation patterns thatrotate around a central filament curve. Starting from thereaction-diffusion equations, I will show that the detailed,instantaneous equations of filament motion heavily dependon the scroll wave’s rotation phase. However, by filteringout epicycle motion we obtain simpler dynamics for a pre-viously unseen companion of the classical filament, whichwe call the ‘virtual filament’. [See H. Dierckx and H. Ver-schelde, Phys. Rev. E 88 0629072013 or arXiv:1311.2782.]

NW14 Abstracts 103

Hans DierckxDepartment of Physics and AstronomyGhent [email protected]

MS47

Dynamics of Spiral Cores: the Effect of Boundariesand Heterogeneities

While reaction-diffusion PDEs used to model cardiac tis-sue respect continuous translational and rotational sym-metries, the cardiac tissue and the spatially discretized nu-merical models based on these PDEs do not. The dynamicsare modified due to both boundary conditions and hetero-geneities associated, for instance, with the cellular struc-ture of the tissue or the computational mesh. This talk willdiscuss the effect of such heterogeneities on the dynamicsof stable and unstable spiral wave solutions.

Roman GrigorievGeorgia Institute of TechnologyCenter for Nonlinear Science & School of [email protected]

Christopher MarcotteGeorgia Institute of [email protected]

Greg ByrneGeorge Mason [email protected]

MS47

Spiral Pinballs

Macroscopic systems exhibiting both wave-like andparticle-like properties have received much attention in re-cent years. One case is excitable media, for which spiralwaves have core regions that behave like particles. Underresonant stimulation, spiral cores drift in straight lines andmay reflect from boundaries in interesting ways. In thistalk, the ‘pinball’ dynamics of these reflections are stud-ied, via numerical simulations and asymptotic theory.

Jacob LanghamMathematics InstituteUniversity of [email protected]

Dwight BarkleyUniversity of WarwickMathematics [email protected]

MS47

Kinematic Theory of Spirals and Wave Segments

Spiral waves and wave segments represent typical exam-ples of self-organized patterns observed in excitable me-dia. We demonstrate that at least two dimensionless medi-ums parameters should be measured to predict the spatio-temporal characteristics of these patterns. The findingsshould be applicable to a wide class of media due to thegenerality of the free boundary approach used. The predic-tions of this approach are in good quantitative agreement

with the results from numerical reaction-diffusion simula-tions.

Vladimir ZykovMax Planck Institute for Dynamics and [email protected]

Eberhard BodenschatzMax Planck Institute for Dynamics & Self-Organizationeberhard.bodenschatz.ds.mpg.de

MS48

Surface Waves in Graded Index Meta-materials

We have studied the properties of electromagnetic surfacewaves in graded index meta-materials. It is known thatin transient layers, where index of refraction changes sign,these surface waves are associated with field enhancementwhich leads to the anomalous absorption. We have stud-ied the nonlinear parametric processes due to such fieldenhancement in case of non collinear incident fields.

Ildar R. GabitovDepartment of Mathematics, University of [email protected]

Andrei MaimistovMoscow Engineering Physics [email protected]

MS48

Models for Laser-Driven Generation of THz Radi-ation

We discuss the generation of THz radiation by two-color ul-trashort optical pulses interacting in a nonlinear medium.Photocurrents driven by tunnel ionization in gases areshown to be responsible for the emission of broadband THzpulses with field amplitude above the GV/m level. Asso-ciated spectra, which can be evaluated semi-analytically,result from constructive interferences of discrete plasmaradiation bursts occurring at the field maxima. Technolog-ical solutions for optimizing THz emission and links withplasma physics are addressed.

Pedro Gonzalez de AlaizaDepartement de Physique Theorique et AppliqueeCEA, DAM, DIF, 91297 Arpajon, [email protected]

Luc BergeDepartement de Physique Theorique et AppliqueeCEA/DAM Ile de [email protected]

MS48

Channel Capacity and Nonlinear Fourier Trans-form in Coherent Fibre-Optic Communications

I will overview recent progress in studies of the Shannoncapacity of nonlinear fibre channels and new opportunitiesoffered by resurrection of the idea of eigenvalue commu-nications in the new context of non-soliton coherent com-munications. Application of the well-known nonlinear ana-logue of the Fourier transform to digital signal processingin coherent optical transmission leads to radically novelapproaches to coding, transmission and processing of in-formation using specific nonlinear properties of the optical

104 NW14 Abstracts

fibre communication channel.

Sergei TuritsynAston University, [email protected]

MS48

Nondecaying Solutions of KdV Equation

We develop the algebraic procedure that makes possible toconstruct the exact bounded but not vanishing at infinitysolutions of integrable nonlinear systems. Multizone solu-tions of the KdV equation are used as a test bed for themethod.

Vladimir E. ZakharovDepartment of Mathematics, University of Arizona,TucsonP.N. Lebedev Physical Institute RAS, Moscow, [email protected]

Dmitry ZakharovCourant Institute of Mathematical SciencesNew York [email protected]

MS49

Modulation Equations for Interacting LocalizedStructures

Employing modulation equations for the approximate de-scription of nonlinear waves is a widespread techniquewhich allows to reduce the analysis of complicated systemsto universal models such as the KdV or the NLS equation.Recently, the interaction of localized structures was ana-lyzed by deriving a set of modulation equations giving aseparate description of internal and interaction dynamics.We briefly review the procedure for PDEs and display thefull analysis for a polyatomic FPU system.

Martina Chirilus-BrucknerUniversity of [email protected]

MS49

Spatially Periodic Patterns, Busse Balloons, andthe Hopf Dance

The Busse balloon is the region in (wavenumber,parameter)-space for which stable spatially periodic pat-terns exist. In the class of singularly perturbed reaction-diffusion systems, the Busse balloon typically has a non-smooth edge where it borders on a family of homoclinicpatterns. Near this edge, the boundary of the Busse bal-loon has a fine-structure of intertwining curves that repre-sent various kinds of Hopf bifucations – as will be explainedand discussed in this talk.


Bjorn De RijkLeiden [email protected]

Jens Rademacher


Frits VeermanOxford [email protected]

MS49

Coherent Structures in a Population Model forMussel-Algae Interaction

We consider a model that describes the interaction of mus-sel biomass with algae in the water layer overlying the mus-sel bed. The model consists of a system of two coupledpdes where both the diffusion and the advection matricesin are singular. We use the Geometric Singular Perturba-tion Theory to capture nonlinear mechanisms of patternand wave formation in this system.

Anna GhazaryanDepartment of MathematicsMiami [email protected]

Vahagn ManukianMiami University [email protected]

MS49

Pattern Formation in a Class of Landau-Lifschitz-Gilbert-Slonczewski Equations for Spintronic De-vices

The Landau-Lifshitz-Gilbert-Slonczewski equation de-scribes magnetization dynamics in the presence of an ap-plied ?eld and a spin polarized current. In the case ofaxial symmetry and with focus on one space dimension,we investigate the emergence of space- time patterns inthe form of coherent structures, whose pro?les asymptoteto wavetrains. In particular, we give a complete existenceand stability analysis of wavetrains and prove existence ofvarious coherent structures, including soliton- and domainwall-type solutions. Decisive for the solution structure isthe size of anisotropy compared with the di?erence of ?eldintensity and current intensity normalized by the damping.This is joint work with Christof Melcher (RWTH).

Jens RademacherUniversity of [email protected]

MS50

Dimension-Breaking Phenomena for SolitaryGravity-Capillary Water Waves

The water-wave problem has small-amplitude line solitary-wave solutions which to leading order are described by theKorteweg-deVries equation (for strong surface tension) ornonlinear Schrodinger equation (for weak surface tension).We present an existence theory for three-dimensional pe-riodically modulated solitary-wave solutions to the water-wave problem which have a solitary-wave profile in thedirection of propagation and are periodic in the trans-verse direction. They emanate from the line solitary wavesin a dimension-breaking bifurcation and are described toleading order by the Kadomtsev-Petviashvili equation (forstrong surface tension) or Davey-Stewartson equation (forweak surface tension). The term dimension-breaking phe-

NW14 Abstracts 105

nomenon describes the spontaneous emergence of a spa-tially inhomogeneous solution of a partial differential equa-tion from a solution which is homogeneous in one or morespatial dimensions.

Mark D. GrovesUniversitat des [email protected]

Shu-Ming SunVirginia TechDepartment of [email protected]


MS50

Lasers and Ripples

Three dimensional capillary-gravity waves behave verymuch like strong laser pulses propagating through a Kerrmedium. We describe the reasons for this similarity andhow the evolution in the two cases differ past the collapsetime.

Paul A. MilewskiDept. of Mathematical SciencesUniversity of [email protected]

Zhan WangUniversity College [email protected]

MS50

The Influence of Surface Tension Upon TrappedWaves and Hydraulic Falls

Steady two-dimensional free-surface flows past submergedobstructions on the bottom of a channel are presented.Both the effects of gravity and surface tension are consid-ered. Critical flow solutions with subcritical flow upstreamand supercritical flow downstream are sought using fullynonlinear boundary integral equation techniques based onthe Cauchy integral formula. When a second submergedobstruction is included further upstream in the flow config-uration trapped wave solutions are found for small valuesof the Bond number, for some values of the Froude num-ber. Other types of trapped waves are found for strongertension when the second obstruction is placed downstreamof the hydraulic fall generated by the first obstacle.

Emilian I. ParauUniversity of East [email protected]

Charlotte PageSchool of Computing SciencesUniversity of East Anglia, Norwich, [email protected]

MS50

Stability of Near-Resonant Gravity-Capillary

Waves

I will present results on the computation and stability ofperiodic surface gravity-capillary waves that are in a near-resonant regime. In the zero amplitude limit, the param-eters defining these solutions almost satisfy the resonancecondition that leads to Wilton ripples. This manifests it-self as a small divisor problem in the Stokes expansion forthese solutions. We compute such solutions and investigatetheir stability using Hills method.

Olga TrichtchenkoDepartment of Applied MathematicsUniversity of [email protected]

Bernard DeconinckUniversity of [email protected]

MS51

CPT-symmetric Spin-orbit-coupled Condensate

We introduce a meanfield model of a spin-orbit-coupledatomic system accounting for pumping and removal ofatoms from the two states, i.e. giving origin to an openspin-orbit-coupled Bose–Einstein condensate. The systempossess charge-parity-time (CPT) symmetry and obeyssuch properties as control of the stability by the externaltrap, singular CPT symmetry phase breaking, the exis-tence of stable nonlinear modes with nonzero currents inrepulsive and attractive condensates, multiple re-enteringthe CPT-symmetric phase, splitting of nonlinear modesinto sets of solitons (wave-packets) moving with differentvelocities and in different directions in the condensate re-leased from the trap.

Yaroslav KartashovInstitut de Ciencies FotniquesBarcelona, [email protected]

Vladimir V. KonotopDepartment of PhysicsUniversity of [email protected]

Dmitry ZezyulinCentro de Fsica Teorica e ComputacionalUniversidade de [email protected]

MS51

Asymmetric Transport in Non-Linear Systemswith Parity-Time Symmetry

We will introduce the notion of Parity-Time (PT) symme-try and present its implications in classical wave propaga-tion. Using integrated optics and electronics as playfieldswe show how one can construct new circuitry designs thatallow for asymmetric transport due to interplay of the novelproperties of PT-symmetry and non-linearity or gyrotropicelements.

Tsampikos KottosWesleyan UniversityDept. of Physics

106 NW14 Abstracts

[email protected]

MS51

Nonlinear Dynamics in PT-Symmetric Lattices

We consider nonlinear dynamics in a finite parity-time-symmetric chain of the discrete nonlinear Schrodinger(dNLS) type. For arbitrary values of the gain and lossparameter, we prove that the solutions of the dNLS equa-tion do not blow up in a finite time but nevertheless, thereexist trajectories starting with large initial data that growexponentially fast for larger times with a rate that is rigor-ously identified. In the range of the gain and loss parame-ter, where the zero equilibrium state is neutrally stable, weprove that the trajectories starting with small initial dataremain bounded for all times. We also discover a new inte-grable configuration of a PT-symmetric dimer and classifyexistence and stability of large-amplitude stationary PT-symmetric nonlinear states. The results to be reported inthis talk were obtained in collaboration with P. Kevrekidis,V. Konotop, and D. Zezyulin.

Dmitry PelinovskyMcMaster UniversityDepartment of [email protected]

MS51

Interactions of Bright and Dark Solitons with Lo-calized PT -Symmetric Potentials

We study collisions of moving nonlinear-Schrodinger soli-tons with a PT -symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Analyti-cal approximations are developed for both bright and darksolitons. In the former case, an essential aspect of the ap-proximation is that it must take into regard the intrinsicchirp of the soliton, thus going beyond the bounds of thesimplest quasi-particle description of the soliton’s dynam-ics. The analytical results are verified by comparison withnumerical simulations. Collisions result in partial reflectionand transmission of incident solitons. Critical velocitiesseparating these outcomes are found by means of numer-ical simulations, and in the approximate analytical form.Exact solutions for the dark soliton pinned by the complexPT -symmetric dipole are produced too.

Boris MalomedTel Aviv University, [email protected]


MS52

Quasi-Determinants and Non Commutative Equa-tions with Pfaffian Type Solutions

For some time, quasi-determinants of wronskian and gram-mian type have been known to provide solutions to somenon-commutative equations, the most famous of which isthe non-commutative KP equation. In this talk we shalluse some of the ideas developed for the non-commutativeKP equation to look at a possible construction for a non-commutative pfaffian which we shall call a ‘quasi-pfaffian’

and consider its properties.

Claire GilsonSchool of Mathematics & Statistics,University of Glasgow, [email protected]

MS52

A Four-component Camassa-Holm Type Hierarchy

We consider a 3×3 spectral problem which generates four-component CH type systems. The bi-Hamiltonian struc-ture and infinitely many conserved quantities are con-structed for the associated hierarchy. Some possible re-ductions are also studied.

Qingping LiuDepartment of Mathematics,China University of Mining and Technoly (Beijing)[email protected]

MS52

On Jost Solutions for the Discrete and Ultradis-crete KdV Equation

Explicit expressions for the Jost solutions of the discreteSchrodinger equation for compact support solution of thediscrete KdV are described. These expressions have ultra-discrete limits and applications of these results to solvingarbitrary initial value problems for the ultra discrete KdVequation using the inverse scattering proposed by Willoxet al (J. Phys. A: Math. Theor. 43 (2010) 482003) areconsidered.

Jonathan NimmoSchool of Mathematics & StatisticsUniversity of Glasgow, [email protected]

MS52

Classification of Tau-symmetric Hamiltonian Evo-lutionary PDEs

We consider the classification of deformations of the dis-persionless KdV hierarchy which possess a Hamiltonianstructure and satisfy the so called tau-symmetry property.We conjecture that such deformations are characterizedby an infinite series of constant parameters, and provideevidences to support this conjecture. We also considerthe classification problem of tau-symmetric deformations ofHamiltonian integrable hierarchies of hydrodynamic type.

Youjin ZhangDepartment of Mathematics,Tsinghua University, [email protected]

MS53

Skyrmions as Models of Nuclei

Skyrmions in 3-dimensions are compact soliton solutions ina nonlinear theory of pions. They have interesting shapes,and several have Platonic symmetry. There is a conservedtopological charge B which is identified with baryon num-ber. Skyrmions are proposed to model protons, neutronsand larger nuclei. I will discuss progress in constructingSkyrmion solutions up to baryon number 108 and beyond,

NW14 Abstracts 107

and finding the properties of their quantised states, includ-ing their spin.

Nicholas MantonDept. of Applied Mathematics and Theoretical PhysicsUniversity of [email protected]

MS53

Vorticity Models in Condensed Matter Physics andGradient Flows of 1-Homogeneous Functionals

We illustrate some recent results on variational and evo-lution problems concerning a certain class of convex 1-homogeneous functionals for vector-valued maps, related tovortex density in 3-d superconductors and superfuids, thatarise as limiting cases of the classical Ginzburg-Landau andGross-Pitaevskii energies. Minimizers and gradient flowsof such functionals may be characterized as solutions ofsuitable non-local vectorial generalizations of the classicalobstacle problem.

Giandomenico OrlandiDepartment of Computer ScienceUniversity of [email protected]

MS53

Long Range Scattering for the Klein-Gordon Equa-tion with Nonhomogeneous Nonlinearities

The asymptotic stability of coherent states , like kinks inone dimension poses new great challenges. This is dueto the long range nature of the dispersive equation. Thistalk will focus on one such problem. We study the 1DKlein-Gordon equation with quadratic and variable coeffi-cient cubic nonlinearity. This problem exhibits a strikingresonant interaction between the spatial frequencies of thenonlinear coefficients and the temporal oscillations of thesolutions. We prove global existence and (in L-infinity)scattering as well as a certain kind of strong smoothnessfor the solution at time-like infinity with the help of severalnew classes of normal-forms transformations. The analysisalso shows the limited smoothness of the solution, in thepresence of the resonances.

Avy SofferRutgers University, Math [email protected]

MS53

Coherent Motion in Hamiltonian Lattices withNext-to-nearest Neighbour Interactions

We consider an infinite chain of particles with nearestneighbour (NN) and next to nearest neighbours (NNN) be-ing coupled by nonlinear springs. To mimic the Lennard-Jones potential, the NN and NNN springs act against eachother. The existence of supersonic periodic solutions isdiscussed, as well as the existence of subsonic waves ho-moclinic to exponentially small periodic oscillations. Thecontrast to the theory for chains with NN interaction aloneis discussed.

Johannes [email protected]

Christine Venney


MS54

Discrete KP Equation with Self-Consistent Sources

We show that the discrete Kadomtsev–Petviashvili (KP)equation with sources, obtained recently by the ”sourcegeneralization” method, can be incorporated into thesquared eigenfunctions symmetry extension procedure.Moreover, using the known correspondence betweenDarboux-type transformations and additional independentvariables, we demonstrate that the equation with sourcescan be derived from Hirota’s discrete KP system of equa-tions (without sources) in a space of bigger dimension. Inthis way we uncover the origin of the source terms as com-ing from multidimensional consistency of the Hirota systemitself.

Adam DoliwaFaculty of Mathematics and Computer ScienceUniversity of Warmia and [email protected]

Runliang LinTsinghua [email protected]

MS54

Discrete Geometry of Polygons and HamiltonianStructures

In this talk I will describe how a discrete moving framedescribing the discrete geometry of polygons in projectiveRPn and other parabolic manifolds describes a Hamilto-nian structure on the space of discrete curvatures. Thestructure is associated to some differential-difference com-pletely integrable systems. In the projective case thesystems are integrable discretizations of generalized KdVequations or AGD flows, systems that posses a realizationas flows of polygons in RPn. This is joint work with JingPing Wang.

Gloria Mari BeffaUniversity of Wisconsin, [email protected]

MS54

Geometric Aspects of Integrable Self-adaptiveMoving Mesh Schemes

We will explain how to construct integrable self-adaptivemoving mesh schemes of some nonlinear wave equationssuch as the short pulse equation and the Camassa-Holmequation. We also show various properties of self-adaptivemoving mesh schemes.

Kenichi MarunoDepartment of MathematicsThe University of Texas-Pan [email protected]

MS54

Discrete Moving Frames and Discrete IntegrableSystems

Discrete moving frame offers significant computational ad-

108 NW14 Abstracts

vantages for our study of discrete integrable systems. Wedemonstrate that the discrete analogues of some curvatureflows lead naturally to Hamiltonian pairs, which gener-ate integrable differential-difference systems. In this talk,we concentrate on the projective space and the integrableequations obtained. This is joined work with ElizabethMansfield and Gloria Mar Beffa.

Jin-Ping WangSchool of Mathematics, Statistics, and Actuarial ScienceUniversity of Kent, [email protected]

MS55

Solitonic and Vortex Behaviour in Exciting Non-linear Hyperbolic Metamaterials


A.D. BoardmanJoule Material & Physics Research Centre,University of Salford, M5 4WT [email protected]

MS55

Nonlinear Wave Propagation and Localization inSquid Metamaterials

rf SQUIDs are strongly nonlinear oscillators exhibitingseveral fascinating properties. Metamaterials comprisingSQUIDs reveal rich electromagnetic behavior, manifestedby tuneability, switching, and multistability. SQUID meta-materials support flux waves, whose nonlinear propagationgenerates subharmonic pass-bands. They also support lo-calized excitations in the form of dissipative breathers, in-vestigated with respect to their generation conditions andtheir evolution. Tetragonal and honeycomb lattices areconsidered, and features of nonlinearity peculiar to eacharray type are identified and discussed.

Nikos LazaridesCrete Center for Quantum Complexity andNanotechnology,Department of Physics, University of [email protected]

George TsironisDepart. Physics, Univ. Crete and FORTHHeraklion 71003, [email protected]

MS55

Dynamical Properties of Parity-Time SymmetricMetamaterials

Synthetic systems with matched gain and loss may be re-alized through parity-time (PT )-symmetric metamaterialsconsisted of split-ring resonator (SRR) dimers, one withloss and the other with equal amount of gain, coupledmagnetically while nonlinearity and gain are introducedthrough tunnel Esaki diodes. In the absense of nonlinear-ity a PT − phase transition occurs with an accompanyingband modification. The presense of noninearity may in-duce nonlinearly localized modes in the form of discretebreathers with the largest part of the total energy con-centrated in two neighboring sites belonging to the samegain/loss dimer. Time-varying gain/loss parameters in-troduce additional control possibilities including reentrant

PT − transitions.

George TsironisDepart. Physics, Univ. Crete and FORTHHeraklion 71003, [email protected]

MS55

Nonlinear Waves in a Homogenized Two-PhaseParticulate Composite Medium

We consider a two-phase, isotropic, nonlinear, particulatecomposite medium whose effective linear permittivity andnonlinear susceptibility are determined by the strong per-mittivity fluctuation theory. Soliton propagation in thehomogenized composite medium is found to obey the com-plex Ginzburg-Landau (CGL) equation. When linear lossis counterbalanced by nonlinear gain, the propagation ofchirped solitons is permitted. These solitons are classi-fied as Pereira-Stenflo bright solitons or Nozaki-Bekki darksolitons. Their propagation regime depends on the volumefraction of the component phases and on the correlationlength of the spatial fluctuation of the dielectric proper-ties in the medium. In the absence of linear and nonlin-ear dissipation, the CGL equation reduces to the nonlinearSchrodinger (NLS) equation, and both types of solitonssimplify to the usual NLS bright and dark solitons. Theexhibited possibility of localization of electromagnetic en-ergy may pave the way for interesting applications employ-ing such composite media in planar multilayered structuressimilar to the ones utilizing temporal solitons and beamsin nonlinear optical media.

Nikolaos L. TsitsasDepartment of InformaticsAristotle University of Thessaloniki University Campus,[email protected]

Akhlesh LakhtakiaDepartment of Engineering Science and Mechanics,Pennsylvania State University, PA 16802-681, [email protected]

Dimitri FrantzeskakisUniversity of [email protected]

MS56

Modeling Combined UV/IR Filamentation

Advances in laser technology allows the creation of intenselight filaments, in particular in the infrared(IR) and ul-traviolet(UV) regimes. A prevailing challenge is to deter-mine conditions on the filament that enhance the possibil-ity of long (kilometer) distance propagation in the atmo-sphere. This requires theoretical studies on filament forma-tion and stability that parallel experimental efforts. Thiswork presents our recent results on the existence and stabil-ity properties of multi-colored (UV/IR) filament/filamentand filament/vortex states. This work is join with D. Wang(U. Vermont), A. Sukhinin, J-C Diels and A. Rasoulof (U.New Mexico. Work is supported by a DOD-MURI grant.

Alejandro AcevesSouthern Methodist University

NW14 Abstracts 109

[email protected]

MS56

Some Fundamental Issues in Internal Wave Dy-namics

One of the simplest physical setups supporting internalwave motion is that of a stratified incompressible Eulerfluid in a channel. This talk will discuss asymptotic mod-els capable of describing large amplitude wave propagationin this environment, and in particular of predicting theoccurrence of self-induced shear instability in the waves’dynamics for continuously stratified fluids. Some curiousproperties of the Euler setup revealed by the models willbe presented.


MS56

Instabilities of Gravity and Capillary Waves on theSurface of the Fluid

We observed numerically and investigated analytically res-onant interactions on the discrete greed of wave vectors,where resonances are never fulfilled exactly. In this reportwe shall concentrate on an interesting and useful case offour wave resonances for standing wave. Standing wave isrelatively easy to generate in experiment. We have shownthat with time such a wave will generate isotropic wavefield, which is important for experiments on wave turbu-lence.

Alexander O. KorotkevichDept. of Mathematics & Statistics, University of NewMexicoL.D. Landau Institute for Theoretical Physics [email protected]

Alexander DyachenkoLandau Institute for Theoretical [email protected]

Vladimir E. ZakharovDepartment of Mathematics, University of Arizona,TucsonP.N. Lebedev Physical Institute RAS, Moscow, [email protected]

MS56

Blowup Dynamics in the Keller-Segel Model ofChemotaxis

The Keller-Segel equations model chemotaxis of bio-organisms. It is relatively easy to show that in the criticaldimension 2 and for mass of the initial condition greaterthan the critical one, the solutions ’blowup’ (or ’collapse’)in finite time. However, understanding the mechanism ofblowup turned out to be a very subtle problem defyingsolution for the long time. This blowup is supposed to de-scribe the chemotactic aggregation of the organisms andunderstanding its mechanism would allow to compare the-oretical results with experimental observations. In this talkI discuss recent results on dynamics of solutions of the (re-duced) Keller-Segel equations in the critical dimension 2which include a formal derivation and partial rigorous re-sults of the blowup dynamics of solutions of these equa-

tions. Our results are confirmed by numerical simulationsand agrees with the formula of Herrero and Velazquez forspecially constructed solutions. The talk is based on thejoint work with S. I. Dejak, D. Egli and P.M. Lushnikov.

Israel Michael SigalDepartment of MathematicsUniversity of [email protected]

MS57

Dynamics of Vortex Filaments and their Stability

I will discuss some progress in determining the nonlinear(orbital) stability type of certain closed solutions of theVortex Filament Equation (VFE), such as finite-gap fila-ments and periodic breathers. The approach is based onthe correspondence between the VFE and the NonlinearSchrodinger equation (NLS), and on the representation ofa natural sequence of constants of motion in terms of NLSsquared eigenfunctions.

Annalisa M. CaliniCollege of CharlestonDepartment of [email protected]

MS57

Vortex Dynamics in Bose-Einstein Condensates:Bifurcations, Chaotic Dynamics and ExperimentalObservations

In this talk, we will revisit the topic of N-vortices in Bose-Einstein condensates (BECs). We will review recent ex-periments including ones of remarkable symmetry-breakingphenomena in cases of co-rotating vortices, as well as ex-plore steady states and configurations of counter-rotatingvortices. Particle models of such systems will give rise toa considerable wealth of: (a) chaotic dynamics; (b) ex-otic states and bifurcation phenomena; (c) connections toclassical polynomials (e.g. Hermite); (d) coarse grainingfeatures (for large N). We will briefly discuss (a)-(d) andprovide some future perspectives.


MS57

TravelingWaves in Holling-Tanner Model with Dif-fusion

We study diffusive Holling Tanner model for wide range ofparameters from the point of view of existence of travelingwaves. We geometrically construct qualitatively differenttraveling waves that include fronts, periodic wave-trainsand solutions that asymptotically connect wave-trains to aconstant state.

Vahagn ManukianMiami University [email protected]

Anna GhazaryanMiami University

110 NW14 Abstracts

[email protected]

MS57

Semi-strong Multipulse Interaction in ReactionDiffusion Systems: The Case of AsymptoticallyWeak Dissipation

We demonstrate the asymptotic stability of semi-strong N-pulse solutions for a class of singularly perturbed reaction-diffusion equations for which the essential spectrum isasymptotically close to the origin. The key step to boththe existence and stability is the semi-group analysis ofa weakly time-dependent family of non-self adjoint opera-tors. We derive a nonlinear normal hyperbolicity conditionthat balances the time dependence of the linear operatorsagainst the rate of dissipation of the essential spectrum.

Keith PromislowMichigan State [email protected]


Tom BellskyArizona State [email protected]

MS58

An Efficient Boundary Integral Method for 3D In-terfacial Flow with Surface Tension: Numerical Re-sults and Numerical Analysis

We introduce an efficient boundary integral method for theinitial value problem for 3D interfacial flow with surfacetension. The method uses a generalized isothermal param-eterization of the free surface, and requires a fast methodfor evaluation of the Birkhoff-Rott integral. We will alsodiscuss a proof of convergence of the method. This is jointwork with Yang Liu, Michael Siegel, and Svetlana Tlupova.

David AmbroseDrexel [email protected]

MS58

A Reduction of the Euler Equations to a SingleTime-Dependent Equation

In this talk, a new single equation for the time-dependentfree-surface of a water-wave under the influence of grav-ity and surface tension is derived. This new equation isderived without approximation from Euler’s Equations foran invicid, irrotational fluid and is valid in two spatial di-mensions (one-dimensional wave surface). Using this singleequation, various asymptotic models are derived. Classicalreduced models such as KdV are found with ease, and newasymptotic models are presented.

Katie OliverasSeattle UniversityMathematics [email protected]

Vishal VasanDepartment of Mathematics

The Pennsylvania State [email protected]

MS58

Gravity Capillary Waves and Related Problems

Nonliinear waves propagating under an elastic membraneare considered. Results for periodic waves, solitary waveswith decaying oscillatory tails and generalised solitarywaves are presented. The results are compared to the clas-sical theory of gravity-capillary waves and new types ofwaves are found and discussed.

Jean-Marc Vanden-BroeckUniversity College [email protected]

MS58

A Quasi-Planar Model for Gravity-Capillary Inter-facial Waves in Deep Water

We propose a quasi-planar model for gravity-capillarywaves between two semi-infinite, immiscible fluids. Ouranalysis and numerics show that there exists a critical den-sity ratio, below which the interfacial solitary waves andthe bifurcation diagram are qualitatively similar to thoseof the free-surface gravity-capillary waves on deep water.However, the bifurcation mechanism near the minimum ofthe phase speed is essentially similar to that of the hydroe-lastic waves on deep water, when the density ratio is in thesupercritical regime.

Zhan WangUniversity College [email protected]

MS59

Solitons in Quadratically Nonlinear Media withPT-Symmetric Potentials

The system of equations for waves in quadratically nonlin-ear media with a parity-time(PT) symmetric modulationof refractive indices for fundamental and second harmonicsare studied. Exact bright and dark solitary solutions forcorresponding forms of the PT-symmetric potentials arefound. Their stability and dynamics are investigated.

Fatkhulla AbdullaevCentro de Fisica Teorica e Computacional,Faculdade de Ciencias, Universidade de [email protected]

Bakhram UmarovInternational Islamic University of MalaysiaKulliyyah of [email protected]

MS59

Nonlinear Quantum Dynamics of a BEC in a PT -symmetric Double-well Trap

The dynamics of a Bose-Einstein condensate in a non-Hermitian PT -symmetric double-well potential modellinga coherent in- and outflux of particles is investigated inthe mean-field limit. The time-dependent Gross-Pitaevskiiequation is solved and it is shown that it exhibits stablestationary states, however, the dynamical properties arevery comprehensive. Elliptically stable and hyperbolically

NW14 Abstracts 111

unstable stationary solutions are found. The complicateddynamical properties can be related to the subtle interplayof the nonlinearity and the non-Hermiticity.

Holger Cartarius, Daniel Haag, Dennis Dast, AndreasLohle, Jorg Main, Gunter WunnerUniversitat [email protected],[email protected], [email protected], [email protected],[email protected], [email protected]

MS59

Dynamical Theory of Scattering for Complex Po-tentials, Inverse Scattering, and Confined Nonlin-earities

For a given possibly complex scattering potential v(x) inone dimension, we construct a two-level non-HermitianHamiltonian whose S-matrix coincides with the transfermatrix of v(x). We use this approach to develop a dynam-ical theory of scattering where the reflection and transmis-sion amplitudes are given as solutions of a set of dynamicalequations and offer an inverse scattering scheme for con-struction of scattering potentials with desirable propertiesat a prescribed wavelength. We will also outline an exten-sion of some of our results to situations where a confinednonlinearity is present.

Ali MostafazadehKoc University, [email protected]

MS59

Partially- PT -symmetric Potentials with All-realSpectra and Soliton Families

Multi-dimensional complex potentials with partial parity-time (PPT ) symmetry are proposed. The usual parity-time (PT ) symmetry requires that the potential is invari-ant under complex conjugation and simultaneous reflectionin all spatial directions. However, we show that if the po-tential is only partially PT -symmetric, i.e., it is invariantunder complex conjugation and reflection in a single spa-tial direction, then it can also possess all-real spectra andcontinuous families of solitons. These results are estab-lished analytically and corroborated numerically. Symme-try breaking of solitons in PPT -symmetric potentials willalso be discussed.

Jianke YangDepartment of Mathematics and StatisticsUniversity of [email protected]

MS60

Lattice Boussinesq Equation and Convergence Ac-celeration Algorithms

In this talk, we will give the molecule solution of an equa-tion related to the lattice Boussinesq equation with the helpof determinantal identities. It is shown that this equationcan for certain sequences be used as a numerical conver-gence acceleration algorithm. Reciprocally, we will derive anon-autonomous form of the integrable equation related tothe lattice Boussinesq equation by a new algebraic method.This method starts from constructing generalizations of

convergence acceleration algorithms related to discrete in-tegrable systems. Then the non-autonomous version of thecorresponding integrable systems are derived. The newoperator generalizing the usual forward difference operatorin this method was first proposed by C. Brezinski whenstudying generalizations of the epsilon algorithm.

Yi HeWuhan Institute of Physics and Mathematics, [email protected]

MS60

Constructing Probabilistic Particle Cellular Au-tomata from Fundamental Diagrams

We propose a probabilistic neighborfood-five particle cel-lular automata (CA) which includes fifteen deterministicparticle CA. The probabilistic particle CA is constructedfrom evolution equations of max-min form obtained fromultradiscrete Cole-Hopf transformation. We also show afundamental diagram of the probabilistic particle CA ob-tained by numerical simulations. Finally we discuss aboutfuture plans.

Junta MatsukidairaRyukoku University, [email protected]

MS60

Soliton Solutions to an Extended Box and Ball Sys-tem Equation

We consider an extended Box and Ball system equation.It has two type of ultradiscrete soliton solutions. One isa solution of the ultradiscrete KdV type and the other isa solution of the ultradiscrete Toda type. We propose asolution which includes both of them.

Hidetomo NagaiTokai [email protected]

MS60

On Exact Solutions to Lattice Equations

We propose dynamical systems defined on algebra of lat-tices, which we call lattice equations. We give exact solu-tions to a class of lattice equations of which complexity ofsolutions are of polynomial order. Moreover we discuss therelationship between those equations and binary cellularautomata.

Daisuke TakahashiWaseda University, [email protected]

MS61

Well-Balanced Positivity Preserving Central-Upwind Scheme for the Shallow Water Systemwith Friction Terms

Shallow water models are widely used to describe and studyfree-surface water flow. While in some practical applica-tions the bottom friction does not have much influenceon the solutions, there are still many applications, wherethe bottom friction is important. In particular, the fric-tion terms will play a significant role when the depth of

112 NW14 Abstracts

the water is very small. In this talk, I will discuss shal-low water equations with friction terms and their approx-imation by a well-balanced central-upwind scheme that iscapable of exactly preserving physically relevant steadystates. The scheme also preserves the positivity of the wa-ter depth. We test the designed scheme on a number ofone- and two-dimensional examples that demonstrate ro-bustness and high resolution of the proposed numerical ap-proach. The data in the last numerical example correspondto the laboratory experiments, designed to mimic the rainwater drainage in urban areas containing houses. Since therain water depth is typically several orders of magnitudesmaller than the height of the houses, we develop a specialtechnique, which helps to achieve a remarkable agreementbetween the numerical and experimental results.

Alina ChertockNorth Carolina State UniversityDepartment of [email protected]

MS61

Well-Balanced Fully Coupled Central-UpwindScheme for Shallow Water Flows over Erodible Bed

Intense sediment transport and rapid bed evolution arefrequently observed under highly-energetic flows, and bederosion sometimes is of the same magnitude as the flowitself. Simultaneous simulation of multiple physical pro-cesses requires a fully coupled system to achieve an ac-curate hydraulic and morphodynamical prediction. In thistalk, I will present a high-order well-balanced finite-volumemethod for a new fully coupled two-dimensional hyperbolicsystem consisting of the shallow water equations with fric-tion terms coupled with the equations modeling the sed-iment transport and bed evolution. The nonequilibriumsediment transport equation is used to predict the sedi-ment concentration variation. Since both bed-load, sed-iment entrainment and deposition have significant effectson the bed evolution, an Exner-based equation is adoptedtogether with the Grass bed-load formula and sedimententrainment and deposition models to calculate the mor-phological process. The resulting 5 by 5 hyperbolic systemof balance laws is numerically solved using a Godunov-typecentral-upwind scheme on a triangular grid. A computa-tionally expensive process of finding all of the eigenval-ues of the Jacobian matrices is avoided: The upper/lowerbounds on the largest/smallest local speeds of propaga-tion are estimated using the Lagrange theorem. A specialdiscretization of the source term is proposed to guaranteethe well-balanced property of the designed scheme. Theproposed fully coupled model is verified on a number ofnumerical experiments.

Abdolmajid Mohammadian, Xin LiuUniversity of [email protected], [email protected]

MS61

MLMC-FVM for Shallow Water Equations withUncertain Bottom Topography

The initial data and bottom topography, used as inputsin shallow water models, are prone to uncertainty due tomeasurement errors. We model this uncertainty statisti-cally in terms of random shallow water equations. We ex-tend the Multi-Level Monte Carlo (MLMC) algorithm tonumerically approximate the random shallow water equa-

tions efficiently. The MLMC algorithm is suitably modifiedto deal with uncertain (and possibly uncorrelated) data oneach node of the underlying topography grid by the useof a hierarchical topography representation. Numerical ex-periments in one and two space dimensions are presentedto demonstrate the efficiency of the MLMC algorithm.

Jonas SukysETH, [email protected]

MS61

High Order Discontinuous Galerkin Methods forthe Shallow Water Equations

Shallow water equations (SWEs) with a non-flat bottomtopography have been widely used to model flows in riversand coastal areas. Since the SWEs admit non-trivial equi-librium solutions, extra care need to be paid to approx-imate the source term numerically. To capture this bal-ance and near-equilibrium solutions, well-balanced meth-ods have been introduced and performed well in many nu-merical tests. In this presentation, we will talk about re-cently developed high-order discontinuous Galerkin (DG)finite element methods, which can capture the general mov-ing steady state well, and at the same time are positivitypreserving without loss of mass conservation. Some nu-merical tests are performed to verify the positivity, well-balanced property, high-order accuracy, and good resolu-tion for smooth and discontinuous solutions.

Yulong XingDepartment of MathematicsUniveristy of Tennessee / Oak Ridge National [email protected]

MS62

Multi-Component Integrable Wave Equations andGeometric Moving Frames

I will survey some recent work giving a geometric approachto deriving group-invariant nonlinear wave equations. Theapproach is based on applying moving-frame methods tocurve flows in geometric spaces, where the differential co-variants of the curve naturally satisfy a multi-componentnonlinear wave equation which has an internal symmetrygroup given by the equivalence group of the moving frame.In this setting there are natural classes of integrable flows,which give rise to group-invariant integrable wave equa-tions with a Lax pair, a bi-Hamiltonian structure, and asymmetry recursion operator.

Stephen AncoDepartment of MathematicsBrock [email protected]

MS62

Some Novel Geometric Realizations of IntegrableHierarchies

We discuss geometric evolution equations for generic curvesin centroaffine 3-space and for Legendrian curves in the3-sphere. In the centroaffine case, we construct a doublehierarchy of mutually commuting curve flows, whose curva-ture evolution equations realize the two-component Boussi-nesq hierarchy. The passage from the velocity components(with respect to a Frenet-type frame) to invariant evolu-tions gives a Poisson operator for the hierarchy. Within

NW14 Abstracts 113

the hierarchy of curve flows there is a sub-family of geo-metric evolution equations that preserves curves on a conethrough the origin, and realize the Kaup-Kuperschmidt hi-erarchy. In the Legendrian case, we can also realize theKaup-Kuperschmidt equations via a sequence of geometricflows.

Thomas IveyCollege of [email protected]

MS62

A Finite Dimensional Integrable System Arising inShock Clustering

In previous work, Menon and Srinivasan studied scalar con-servation laws with convex flux and initial datum given byspectrally negative Feller processes. For the special casein which the initial condition is stationary, it was shownthat the generator of the Feller process evolves accordingto a Lax equation. Subsequently, Menon introduced a fi-nite dimensional version of this problem, associated withthe Markov group. In this talk, we will explain how tosolve this finite dimensional system explicitly.

Luen-Chau LiDepartment of MathematicsPennsylvania State University, [email protected]

MS62

Integrable Systems and Invariant Geometric Flowsin Similarity Symplectic Geometry

In this talk, differential invariants and invariant geometricflows in similarity symplectic geometry are studied. Ex-plicit formulae of symplectic invariants and Frenet formu-lae for curves in the similarity symplectic geometry areobtained by the moving frame method. The relationshipbetween the of Euclidean symplectic invariants and simi-larity symplectic invariants is also identified. As a result,we show that the matrix mKdV equation and the matrixBurgers equation arise from invariant nonstreching curveflows in the similarity symplectic geometry.

Changzheng QuNorthwest University, [email protected]

MS63

Quasi-Discrete Solitons in Nonlinear TransmissionLine Metamaterials


D.J. FrantzeskakisUniversity of Athens, Zografos, [email protected]

MS63

Amplitude Modulation and Envelope Mode For-mation in Left-Handed Media: a Survey of RecentResults


Ioannis KourakisQueen’s University Belfast

Centre for Plasma Physics (CPP)[email protected]

MS63

Pt-Symmetry and Embedded Modes in the Con-tinuum for Magnetic Metamaterials

First, we examine the PT-symmetry breaking transitionfor a magnetic metamaterial of a ?nite extent, modeled asan array of coupled split-ring resonators in the equivalentcircuit model approximation. Small-size arrays are solvedcompletely in closed form, while for arrays larger than N =5 results were computed numerically for several gain/lossspatial distributions. In all cases, it is found that the pa-rameter stability window decreases rapidly with the sizeof the array, until at N = 20 approximately, it is not pos-sible to support a stable PT-symmetric phase. A simpleexplanation of this behavior is given. Next, we consider theproblem of building a surface localized mode embedded inthe continuous band of a semi-infinite one- dimensional ar-ray of split-ring resonators. We suggest an efficient methodfor creating such surface mode and the local bounded po-tential necessary to support this mode.

Mario MolinaDepartamento de Fisica, Universidad de ChileSantiago, [email protected]

MS64

High-Frequency Instabilities of Small-AmplitudeSolutions of Hamiltonian PDEs

Generalizing ideas of MacKay, and MacKay and Saffman, anecessary condition for the presence of high-frequency (i.e.,not modulational) instabilities of small-amplitude solutionsof Hamiltonian partial differential equations is presented,entirely in terms of the Hamiltonian of the linearized prob-lem. The entire theory with the exception of a Krein sig-nature calculation can be phrazed in terms of the disper-sion relation of the linear problem. The general theorychanges as the Poisson structure of the Hamiltonian PDEis changed. Two important cases are worked out and dif-ferent examples are presented.

Bernard DeconinckUniversity of [email protected]

MS64

Multipole and Half-vortex Gap-solitons in Spin-orbit Coupled Bose-Einstein Condensates

Using the parity and time reversal symmetries of a two-dimensional spin-orbit coupled Bose-Einstein condensatein a Zeeman lattice, we found numerically various familiesof localized solutions, including multipole and half-vortexsolitons. The obtained solutions may exist at any directionof the gauge field with respect to the lattice and can befound either in finite gaps. The existence of half-vorticesrequires higher symmetry. Stability of these modes makesthem feasible for experimental observation.

Yaroslav KartashovInstitut de Ciencies FotniquesBarcelona, [email protected]

114 NW14 Abstracts

Vladimir V. KonotopDepartment of PhysicsUniversity of [email protected]

Valery LobanovInstitut de Ciencies FotoniquesBarcelona, [email protected]

MS64

Wave Turbulence: A Story Far from Over

Despite some successes, there are still many open questionsas to the validity of the wave turbulence closure and therelevance of Kolmogorov-Zakharov finite flux solutions. Insome cases, such as gravity driven water waves, the KZspectrum has to be augmented with the Phillips’ spectrumat high wavenumbers. Why? In others, such as the theMMT equation, the KZ spectrum and indeed the wholeclosure does not obtain at any scale at all. Why? Furtherwe ask: might it be possible to give a priori conditions onweakly nonlinear systems so that one is guaranteed that atleast the natural asymptotic closure holds? I look forwardto addressing and discussing these challenges.

Alan NewellUniversity of ArizonaDepartment of [email protected]

MS64

Energy Growth in Switching Hamiltonian Systemsof Fermi-Ulam Type

A natural example of a switching Hamiltonian system ofFermi-Ulam type (a particle bouncing between two oscillat-ing walls) is considered. A corresponding smooth in timesystem would possess invariant KAM tori which would pre-vent energy growth. Numerical simulations suggest thatenergy does not grow even in the discontinuous case. Weexplain this phenomenon using relation with another prob-lem considered earlier by Kesten.

Vadim ZharnitskyDepartment of MathematicsUniversity of [email protected]

Maxim ArnoldUniversity of Illinois at Urbana-ChampaignDepartment of [email protected]

MS65

Dynamics of Cavity Solitons and Optical FrequencyCombs in the Lugiato-Lefever Equation

Kerr frequency combs can be modeled in a similar way astemporal cavity solitons (CSs) in nonlinear cavities, usingthe Lugiato-Lefever equation describing pattern formationin optical systems. Here, we first characterize differentdynamical regimes of CSs, such as time-periodic oscilla-tions and various chaotic dynamics. Secondly, the effect ofthird order dispersion on the stability and snaking struc-ture of CSs is studied. Finally, we discuss how the dynam-

ics change as the cavity size decreases.

Lendert GelensStanford [email protected]

Pedro Parra-RivasApplied Physics Research GroupVrije Universiteit Brussel, [email protected]

Damia GomilaIFISC-CSIC, Universitat de les Illes BalearsPalma de Mallorca, [email protected]

Francois LeoPhotonics Research Group,Ghent University, [email protected]

Stephane CoenDepartment of Physics, University of Auckland,New [email protected]

MS65

Localised Hexagon Patches on the Surface of aMagnetic Fluid

We present experimental results showing the existence ofa patches involving different numbers cellular hexagons onthe surface of a magnetic fluid under the influence of avertical magnetic field. These patches are spontaneouslygenerated by jumping into the neighborhood of the unsta-ble branch of the domain covering hexagons and are foundto co-exist in the same parameter region. Using numer-ical continuation techniques, we investigate the existenceof localized hexagons in the full equations determining thefree-surface of magnetic fluid and describing the experi-ment. We find that cellular hexagons possess a Maxwellpoint where the energy of a single hexagon is equal to theenergy of the flat state providing an energetic explanationfor the multitude of various different hexagon patches ob-served in experiments. Furthermore, it is found that planarhexagon fronts and hexagon patches undergo homoclinicsnaking.

David LloydUniversity of [email protected]

Reinhard RichterUniversity of [email protected]

MS65

Localized Solutions in Plane Couette Flow with Ro-tation

Localized solutions of plane Couette flow (PCF) bifurcatefrom the subcritical 3D periodic state at infinite parameter;forcing the system through rotation changes this. The 3Dperiodic state now emerges secondarily from a 2D periodicstate, making the localized solution a 3D patch embeddedin a 2D patterned background. The nontrivial backgroundhas some effect, however much of the scenario seen in other

NW14 Abstracts 115

systems remains, such as the snakes-and-ladders structurealready found in non-rotating PCF.

Matthew SalewskiMax Planck Institute for Dynamics andSelf-Organization, Ger

{E}cole Polytechnique F{e}d{e}rale de Lausanne, [email protected]

Tobias SchneiderMax Planck Institute for Dynamics and Self-Organization,[email protected]

MS65

Stability Properties of Localized Structures NearSnaking

Snaking refers to the existence of localized roll structures inspatially extended, reversible 1D partial differential equa-tions, that exist along a vertical sine-shaped bifurcationcurve so that the width of the underlying periodic roll pat-tern increases along the bifurcation curve. Localized rollsundergo a series of bifurcations along the branch, and thistalk is concerned with analytical and numerical aspects oftheir PDE stability spectra.

Elizabeth J. MakridesBrown UniversityDivision of Applied Mathematicselizabeth [email protected]

Bjorn SandstedeBrown Universitybjorn [email protected]

MS66

Modeling Capillary Origami

To continue the move towards miniaturization in technol-ogy, developing new methods for fabricating micro- andnanoscale objects has become increasingly important. Onepotential method, called capillary origami, consists of plac-ing a small drop of liquid on a thin, inextensible sheet. Inthis state the system minimizes its total energy, pullingthe planar sheet upward. Under appropriate conditionsthe sheet will fully encapsulate the liquid, creating a three-dimensional structure. In this talk, we discuss recent workon modeling a two-dimensional version of this system.

Nicholas D. BrubakerUniversity of [email protected]

MS66

The Stability and Evolution of Curved DomainsArising from One Dimensional Localized Patterns

In many pattern forming systems, narrow two dimensionaldomains can arise whose cross sections are roughly onedimensional localized solutions. This talk will present aninvestigation of this phenomenon for the variational Swift-Hohenberg equation. Stability of straight line solutions isanalyzed, leading to criteria for either curve buckling orcurve disintegration. A high order matched asymptoticexpansion reveals a two-term expression for the geometricmotion of curved domains which includes both elastic andsurface diffusion-type regularizations of curve motion. Thisleads to novel equilibrium curves and space-filling pattern

proliferation. A key ingredient in the generation of thelabyrinthine patterns formed, is the non-local interactionof the curved domain with its distal segments. Numericaltests are used to confirm and illustrate these phenomena.document or other high-level commands.

Alan E. LindsayApplied Computational Mathematics and StatisticsUniversity of Notre [email protected]

MS66

Hotspots in a Non-Local Crime Model

We extend the Short et al. burglary hotspot model to allowfor a larger class of criminal movement. Specifically, weallow criminals to travel according to a Levy flight ratherthan Brownian motion. This leads to a non-local systemof differential equations. The stability of the homogeneousstate is studied both numerically and through a Turing-type analysis. The hotspot profiles are then constructed toleading order in a singular regime.

Scott McCallaUniversity of California Los [email protected]

Jonah BreslauPomona [email protected]

Sorathan ChaturapruekHarvey Mudd Collegetum [email protected]

Theodore KolokolnikovDalhousie [email protected]

Daniel YazdiUniversity of California, Los [email protected]

MS66

Slowly Varying Control Parameters, Delayed Bi-furcations, and the Stability of Spikes in Reaction-diffusion Systems

We present three examples of delayed bifurcations for spikesolutions of reaction-diffusion systems. The delay effectresults as the system passes slowly from a stable to un-stable regime, and was previously analysed in the contextof ODE’s in [P.Mandel and T.Erneux, J.Stat.Phys 48(5-6)pp.1059-1070, 1987]. Analysis of explicitly solvable nonlo-cal eigenvalue problems allows for analytic predictions ofthe magnitude of delay. Asymptotic results are comparedfavorably to numerical computations.

Justin C. TzouDalhousie [email protected]

Michael WardDepartment of MathematicsUniversity of British [email protected]

Theodore Kolokolnikov

116 NW14 Abstracts

Dalhousie [email protected]

MS67

In-Cavity Transformations for New NonlinearRegimes of Pulse Generation in Mode-Locked Fi-bre Lasers

We review recent progress in the research on nonlinearmechanisms of pulse generation in passively mode-locked fi-bre lasers. These include parabolic self-similar pulse mode-locking, a mode-locking regime featuring pulses with a tri-angular distribution of the intensity, and spectral compres-sion arising from nonlinear pulse propagation. We alsoreport on the possibility of achieving various regimes ofadvanced temporal waveform generation in a mode-lockedfibre laser by inclusion of a spectral filter into the lasercavity.

Sonia BoscoloAston University, Birmingham, United [email protected]

Sergei K. TuritsynAston [email protected]

Christophe FinotUniversite’ de Bourgogne, Dijon, [email protected]

MS67

Mechanisms and Definitions of Rogue Waves inNonlinear Systems

Optical rogue waves are rare yet extreme fluctuations inan optical field. First used to describe an analogy betweenwave propagation in optical fibre and on deep water, theterminology has since been generalized to many other op-tical processes. We present here an overview of recent re-search in this field, and although statistical features areoften considered defining feature of rogue waves, we em-phasize the underlying physical mechanisms driving theappearance of extreme events.

John DudleyUniversite de Franche-Comte, Institut FEMTO-ST, UFRSciences16, route de Gray, 25030 Besancon Cedex, [email protected]

Goery GentyTampere University of TechnologyTampere, [email protected]

Frederic DiasUniversity College DublinSchool of Mathematical [email protected]

MS67

Nonlinear Pulse Shaping in Normally DispersiveFibres: Experimental Examples

While the combination of Kerr nonlinearity with disper-sion in optical fibers can seriously impair high speed op-

tical transmissions, it also provides an attractive solutionto generate new temporal and spectral waveforms. We ex-plain in this talk how to take advantage of the progressivetemporal and spectral reshapings that occur upon propaga-tion in a normally dispersive fiber. We base our discussionon several experimental results obtained at telecommuni-cation wavelengths.

Kamal Hammani, Julien FatomeUniversity of [email protected], [email protected]

Guy MillotUniversity of BourgogneInstitut Carnot de [email protected]

Sonia BoscoloAston University, Birmingham, United [email protected]

Herve RigneaultInstitut [email protected]

Stefano WabnitzUniversity of Brescia, Brescia, [email protected]

Christophe FinotUniversite’ de Bourgogne, Dijon, [email protected]

MS67

Time Domain Nonlinear Structures and Substruc-tures for Ultrafast Photonics

Applications of the time domain amplitude and phasestructures and substructures, induced by self- and cross-phase modulation, phase addition and CARS type pro-cesses, are presented based on our numerical and exper-imental studies. The report is focused on the techniques oftemporal lensing- spectral compression, Fourier conversion-spectrotemporal imaging and frequency tuning, the speci-ficity of Newton rings in a similariton-induced time lens,as well as on nonlinear-optic applications of the trains pe-riodically substructured by similaritons superposition.

Levon Mouradian, Aram Zeytunyan, Hrach Toneyan,Garegin YesayanYerevan State University, Yerevan, [email protected], [email protected],[email protected], [email protected]

Ruben ZadoyanTechnology & Applications Center, Newport Corporation,[email protected]

Frederic Louradour, Alain BarthelemyXLIM-UMR 6172 Universite de Limoges/CNRS, [email protected], [email protected]

MS68

Complex and Coupled Complex Short Pulse Equa-tions: Integrability, Discretization and Numerical

NW14 Abstracts 117

Simulations

We propose a complex and a coupled complex short pulseequations which describe the ultra-short pulse propaga-tion in optical-fibers. After showing the integrabilityof these equations by Lax pairs, we derive the multi-soliton solutions expressed in pfaffians by Hirotas bilinearmethod. In the second partod the talk, the integrable semi-discretizations are constructed and are successfully usedas self-adaptive moving methods for the numerical simula-tions of these equations. This is a collaborative work withK. Maruno and Y. Ohta.

Bao-Feng FengMathematics Department, the University of Texas-PanAmerican1201 W. University Dr., Ediburg TX [email protected]

MS68

A New Procedure to Approach Integrable Dis-cretization

In this talk, we present a new procedure to derive discreteanalogues of integrable PDEs in Hirota’s bilinear formal-ism. This new approach is mainly based on introdutionof suitable auxiliary equations with additional discrete in-dependent variables such that there is integrable compat-ibility between the integrable system under considerationand the new introduced equations while keeping the dis-crete independent variables converging to original ones.We apply this procedure to several equations, includingthe Korteweg-de-Vries (KdV) equation, the Kadomtsev-Petviashvili (KP) equation, the Boussinesq equation, theSawada- Kotera (SK) equation, the Ito equation and etc.,and obtain their associated semi-discrete or fully discreteanalogues. In the continuum limit, these discrete analoguesconverge to their corresponding smooth equations.

Xing-Biao HuAMSS, Chinese Academy of Sciences,[email protected]

MS68

Rogue Waves for Some Soliton Equations

For some soliton equations, the rogue wave solutions arestudied and their algebraic structures are analyzed basedon the bilinear technique of soliton theory.

Yasuhiro OhtaDepartment of MathematicsKobe [email protected]

MS68

New Results on the Explicit Monge-Taylor Formsfor Submanifolds Under Group Actions UsingEquivariant Moving Frame Method

Motivated by the widely used equivariant moving framemethod and starting from the relations between the in-finitesimal generators of transformation groups and theuniversal recurrence formulae for differential invariants, weelaborate important propositions which indicate the pro-cedure to construct more higher order fundamental nor-malized differential invariants such that we can derive theexplicit Monge-Taylor forms extensively for submanifoldsunder group actions. At the same time, a complete set of

syzygies on the generating set of differential invariants areobtained.

Ruoxia YaoSchool of Computer Science, Shaanxi Normal UniversityXi’an, [email protected]

MS69

Well-Balanced Positivity Preserving Cell-VertexCentral-Upwind Scheme for Shallow Water Flows

I will present a novel two-dimensional central-upwindscheme on cell-vertex grids for shallow water equationswith source terms due to bottom topography. This type ofcomputational cells has the advantage of using more cellinterfaces which provide more information on the wavespropagating in different directions. We prove that the pro-posed method is well-balanced and guarantees the positiv-ity of the computed water depth. Our numerical experi-ments confirm stability, well-balanced and positivity pre-serving properties of the proposed method. This schemecan be applied to shallow water models when the bed to-pography is discontinuous and/or highly oscillatory, and oncomplicated domains where the use of unstructured gridsis advantageous.

Abdelaziz BeljadidUniversity of [email protected]

MS69

RVM Finite Volume Methods: Applications toMultilayer Shallow Flows

A new class of incomplete Riemann solvers for the numeri-cal approximation of conservative and nonconservative hy-perbolic systems is proposed. They are based on viscositymatrices obtained by rational approximations to the Jaco-bian of the flux evaluated at some average state, and onlyrequire the knowledge of the maximal characteristic speed.The proposed schemes are applied to nonconservative mul-tilayer shallow water systems, where it has been observedthat intermediate waves can be properly captured for anappropriate degree of approximation of the generating ra-tional function used. The numerical tests indicate that theschemes are robust, running stable and accurate with asatisfactory time step restriction, and the computationalcost is more advantageous with respect to schemes using acomplete spectral decomposition of the Jacobians.

Jose M. GallardoUniversity of Malaga. [email protected]

Manuel CastroUniversity of [email protected]

Antonio MarquinaUniversity of [email protected]

MS69

Path-Conservative Central-Upwind Schemes forNonconservative Hyperbolic Systems

I will present a new path-conservative central-upwind

118 NW14 Abstracts

scheme for noncoservative hyperbolic systems of PDEs.Such systems arise in a variety of applications and the mostchallenging part of their numerical discretization is a robusttreatment of nonconservative product terms. Godunov-type central-upwind schemes were developed as an effi-cient, highly accurate and robust “black-box’ solver forhyperbolic systems of conservation laws. They were suc-cessfully applied to a large number of hyperbolic systemsincluding such nonconservative systems as two-layer shal-low water equations, compressible two-phase flow models,Savage-Hutter type system modelling submarine underwa-ter slides. To overcome the difficulties related to the pres-ence of nonconservative product terms, several special tech-niques were proposed. However, none of these techniqueswas sufficiently robust and thus the applicability of theoriginal central-upwind scheme was quite limited. We haverecently realized that the main drawback of the originalapproach was the fact that the jump of the nonconserva-tive product terms across cell interfaces has never beentaken into account. Rewriting central-upwind schemesin the form of path-conservative schemes has helped tounderstand how the nonconservative products should bediscretized so that their influence on the numerical solu-tion is accurately taken into account. The resulting path-conservative central-upwind scheme is a new robust tool forboth conservative and nonconservative hyperbolic systems.The new scheme has been applied to the Saint-Venant sys-tem with discontinuous bottom topography, two-layer shal-low water system, and the two-mode shallow water equa-tions which was recently derived as a simplified model tatdescribes nonlinear dynamics of waves with different ver-tical profiles. Our numerical results illustrate a superbperformance of the new path-conservative central-upwindscheme, its robustness and ability to achieve very high res-olution.

Alexander KurganovTulane UniversityDepartment of [email protected]

MS69

Well-Balanced Ale: a Dynamic Mesh AdaptationStrategy for Shallow Water Flows

We discuss an efficient and cost effective strategy towarddynamic unstructured mesh adaptation for shallow waterflows. The method combines a mesh movement strategybased on a solution dependent Lapacian operator with anALE formulation. The first provides nodal displacementsdependent on the smoothness of the solution, while the sec-ond allows to follow these solution adaptive displacementswithout the need of any interpolation. We will discuss theconditions allowing the ALE formulation to remain wellbalanced, and show validation on both smooth and discon-tinuous shallow water flows.

Mario [email protected]

MS70

Integrable Nature of Modulational Instability

The modulational instability (MI), known as Benjamin-Feir instability in water waves, is one of the mostwidespread phenomena in nonlinear science. In manycases, the underlying dynamics is governed by the non-linear Schrodinger (NLS) equation. The initial stage of MI

can therefore be described by linearizing the NLS equationaround a constant background. Once the perturbationshave grown to O(1), however, the linearization ceases tobe valid. On the other hand, the NLS equation is a com-pletely integrable infinite-dimensional Hamiltonian system,and the initial-value problem is therefore amenable to so-lution via the inverse scattering transform (IST). In thistalk we will describe how the recently-developed IST forthe focusing NLS equation with non-zero boundary condi-tions can be used to elucidate the nonlinear stage of theMI.


Emily FagerstromState University of New York at [email protected]

MS70

Rational Solitons of Wave Resonant-InteractionModels

Integrable models which describe the resonant interactionof two or more waves in 1 + 1 dimensions are known tobe of applicative interest in many fields. We consider asystem of three coupled wave equations which includesas special cases the vector Nonlinear Schroedinger equa-tions (or Manakov System) and the equations describingthe resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied underthe condition that the solutions have rational, or mixedrational-exponential, dependence on coordinates. Our al-gebraic construction relies on nilpotent matrices and theirJordan form. We systematically search for all bounded ra-tional (mixed rational-exponential) solutions. Rogue wavesof the three-wave resonant interaction equations belog tothis class.

Sara LombardoApplied Mathematics, CEISNorthumbria [email protected]

Antonio DegasperisDipartimento di Fisica, Universita’ La Sapienza, Roma,[email protected]

MS70

On the Spectrum of the Defocusing NLS Equationwith Non-zero Boundary Conditions

We revisit the scattering problem for the defocusing nonlin-ear Schrodinger equation with constant, non-zero bound-ary conditions at infinity. After reviewing some aspectsof the general theory, we consider a specific kind of piece-wise constant potentials to address and clarify two issues,concerning: (i) the (non)existence of an area theorem re-lating the presence/absence of discrete eigenvalues to anappropriate measure of the initial condition; and (ii) theexistence of a contribution to the asymptotic phase differ-ence of the potential from the continuous spectrum.

Barbara PrinariUniversity of Colorado, Colorado SpringsUniversity of Salento, Lecce (Italy)

NW14 Abstracts 119

[email protected]


MS70

Closed Form Solutions of the Hirota Equation

By using the Inverse Scattering Transform we construct anexplicit multisoliton solution formula for the Hirota equa-tion. The formula obtained allows one to get, as particularcases, the N -soliton solution, the breather solution and,most relevantly, a new class of solutions called multipolesoliton solutions. By adapting the Sym-Pohlmeyer recon-struction formula to the Hirota equation, we use these ex-act solutions to study the motion of a vortex filament in anincompressible Euler fluid with nonzero axial velocity. Theresults are obtained in collaboration with G. Ortenzi (Uni-versity of Milano Bicocca) and F. Demontis (University ofCagliari)

Cornelis Van der MeeDipartimento di Matematica e InformaticaUniversita di Cagliari, [email protected]

MS71

Localized Waves in Fully Nonlinear Media

We discuss properties of localized waves in a class of Hamil-tonian lattices involving fully nonlinear interactions. Thisproblem arises for the study of impact propagation in gran-ular chains, where the Hertz contact force introduces afully nonlinear coupling. In this context, new types ofstrongly nonlinear modulation equations such as the loga-rithmic KdV and discrete p-Schrodinger equations can beintroduced. We review open problems concerning localizedwaves in these systems and the original lattice.

Guillaume JamesLaboratoire Jean Kuntzmann, Universite de Grenobleand [email protected]

MS71

New Solutions for Slow Moving Kinks in a ForcedFrenkel-Kontorova Chain

In order to study effects of discreteness on dislocation mo-tion, we construct new traveling wave solutions of mov-ing kink type for a modified, driven, dynamic Frenkel-Kontorova model, representing dislocation motion understress. Formal solutions known so far are inadmissible forvelocities below a threshold value. The new solutions fillthe gap left by this loss of admissibility. Analytical andnumerical evidence is presented for their existence; how-ever, dynamic simulations suggest that they are probablyunstable. We discuss ramifications of this result for slowdislocation motion.

Phoebus RosakisApplied MathematicsUniversity of Crete (Greece)

[email protected]

MS71

On the Travelling Wave Problem for Phase Transi-tions in the Fermi-Pasta-Ulam Chain

We want to present established and recent results on theanalyse of travelling waves for a lattice model of phase tran-sitions. In particular we consider a bistable model with apiece-wise quadratic interaction potential and a smoothedvariant with small spinodal region. Various authors havebeen able to prove in both cases the existence of families ofsubsonic travelling waves, so that special interest is focus-ing on relevant selection criteria to identify meaningful so-lutions. Following ideas from vanishing viscosity approachto conservation laws we present ideas to analyse the stabil-isation of waves in the model with dissipation and discusshow this might help to set up a framework for the inter-pretation of the various types of wave solutions existing forthe lattice problem. This is joint work with M Herrmann,K Matthies, J Zimmer

Hartmut SchwetlickUniversity of BathDepartment of Mathematical Scienceshartmut schwetlick ¡[email protected]¿

MS71

Breathers in Two-dimensional Fermi-Pasta-UlamLattices

Motivated by the observations of Marin et al [Phys Lett A,281, 21, (2001)], we use asymptotic analysis to approximatebreathers in a square, triangular and honeycomb Fermi-Pasta-Ulam lattices. In scalar two-dimensional systems weobtain perturbed 2D NLS equations and conditions on theexistence of breathers. We discuss the open problems ofbreathers’ stability (or decay rate), and interaction prop-erties.

Jonathan WattisSchool of Mathematical SciencesUniversity of [email protected]

MS72

Branch Cut Singularity of Stokes Wave

Stokes wave is the fully nonlinear gravity wave propagatingwith the constant velocity. We consider Stokes wave inthe conformal variables which maps the domain occupiedby fluid into the lower complex half-plane. Then Stokeswave can be described through the position and the type ofcomplex singularities in the upper complex half-plane.Weidentified that this singularity is the square-root branchpoint. We reformulated Stokes wave equation through theintegral over jump at the branch cut which provides theefficient way for finding of the explicit form of Stokes wave.

Pavel M. LushnikovDepartment of Mathematics and StatisticsUniversity of New [email protected]

MS72

Solitons, Self-Induced Transparency, and Quantum

120 NW14 Abstracts

Cascade Lasers

Self-induced transparency is a phenomenon in which anoptical pulse passes through a resonant medium withoutbeing absorbed because of quantum coherence. This phe-nomenon is modeled mathematically using the Maxwell-Bloch equations, and these equations have exact solitonsolutions in the limit that the quantum coherence timesbecome infinite. In this talk, we show that it is possible touse this phenomenon to modelock a quantum cascade laserby creating dissipative solitons.


Muhammad TalukderBUET, Dhaka, [email protected]

MS72

On Multi-Dimensional Compact Patterns

Solitons, kinks or breathers, are manifestations of weaklynonlinear excitations in dispersive media like mass-particlelattices. In a strongly anharmonic chains, the tails ofthe solitary patterns rather than exponentially, decay ata doubly-exponential rate which in the continuum limitcollapse into a singular surface with the resulting wavesbecoming strictly compact,hence their name: compactons.Using the Z-K, the sub-linear Complex Klein-Gordon andthe sub-linear NLS eqs. as examples, we shall demonstratehow N-dimensional compactons emergence and interact. Ingeneral, for compact, and hence non-analytical, structuresto emerge, the underlying system has to undergo a localloss of uniqueness due to, for instance, a degeneracy ofthe highest order operator or other, singularity inducing,mechanisms. For a basic introduction see: What is a Com-pacton, Notices of the AMS, Vol. 52, #7, pp 738, 2005.

Philip RosenauSchool of Mathematical SciencesTel-Aviv University, [email protected]

MS72

Thresholds and Blow-up Dynamics in the Nonlin-ear Dispersive Equations

We consider the focusing nonlinear Schrodinger equationwith finite energy initial data in the mass-supercriticalregime. We discuss the contracting sphere blow-up dynam-ics (joint work with Justin Holmer and Galina Perelman),then present a new dichotomy for scattering and collapsesolutions with finite variance (joint work with ThomasDuyckaerts). In both results solutions can have an arbi-trary L2-norm (mass). Generalization to other nonlineardispersive equations will be considered.

Svetlana RoudenkoThe George Washington [email protected]

MS73

Localised Solutions in Integral Neural Field Equa-tions

I will discuss the formation of stationary localised solutions

in integral neural field models with inhomogeneous synap-tic kernels and Heaviside firing rate functions. We considera simple periodic modulation in the synaptic kernel, applyinterface methods to the resulting integral problem andshow how to construct localised bumps with a finite activ-ity region and two threshold crossings. Localised solutionsare arranged in a ”snake and ladder” bifurcation diagram.However, in this context, interface methods allow for theexplicit construction of a bifurcation equation for localisedsteady states, so that analytical expressions for snakes andladders can be derived. Similarly, eigenvalue computationscan be carried out analytically to determine the stabilityof the solution profiles. In addition, we find regions ofparameter space where the trivial homogeneous state co-exists with two other stable solutions, an above-thresholdperiodic state and a cross-threshold periodic state. Weshow how the multiple stability affects the correspondingbifurcation diagram and examine models in which the fir-ing rate is a steep sigmoid as opposed to the Heaviside stepfunction. This is joint work with Helmut Schmidt (Exeter)

Daniele AvitabileSchool of Mathematical SciencesUniversity of [email protected]

MS73

Localized Convection in a Rotating Fluid Layer

We study stationary convection in a two-dimensional fluidlayer rotating around the vertical and heated from below.With stress-free boundary conditions, spatially localizedstates are embedded in a self-generated background shearzone and lie on a pair of intertwined solution branches ex-hibiting ”slanted snaking”. Similar solutions with no-slipboundary conditions are computed. They are not embed-ded in a background shear and the solution branches ex-hibit snaking without a slant. Homotopic continuationfrom free-slip to no-slip boundary conditions is used totrack the changes in the properties of the solutions andthe associated bifurcation diagrams.

Cedric BeaumeUC [email protected]

MS73

Steady and Oscillatory Localised States in Boussi-nesq Magnetoconvection

Previous studies have shown that it is possible tofind steady, localised convective cells in two-dimensionalBoussinesq magnetoconvection. Building on earlier work,we demonstrate the existence of oscillatory localised con-vective states in this system. We discuss the properties ofthese solutions as well as the effects of changing the hor-izontal boundary conditions. In particular, we show thatthe inclusion of impermeable sidewalls can lead to forma-tion of localised “wall” modes.

Paul J. BushbyNewcastle UniversityUnited [email protected]

Matthew BuckleyNewcastle University

NW14 Abstracts 121

[email protected]

MS73

Moving Localized Structures in a Doubly DiffusiveSystem

In this talk we will describe the origin and properties ofmoving spatially localized structures in natural doubly-diffusive convection in a vertically extended cavity. Thesesolutions arise through secondary parity breaking bifurca-tions. Both single pulse and multipulse states of this typewill be described. The numerical results will be relatedto the phenomenon of homoclinic snaking in spatially re-versible systems.

David Lo JaconoUniversite de [email protected]

Alain BergeonUniversite de Toulouse, [email protected]

Edgar KnoblochUniversity of California at BerkeleyDept of [email protected]

MS74

Isometric Immersions and Pattern Formation inNon-Euclidean Elastic Sheets

Swelling thin elastic sheets are archetypical examples ofpattern forming systems which are often modeled as theminimum an elastic energy which is the sum of a strongstretching energy which penalizes deviations from a growthinduced geometry and a weak bending energy. A funda-mental question is whether we can deduce the three dimen-sional configuration of the sheet given exact knowledge ofthe imposed geometry. Using a combination of rigorousanalysis and numerical conjectures on I will argue that theperiodic patterns observed in nature correspond to low en-ergy isometric immersions of the imposed geometry.

John A. GemmerBrown Universityjohn [email protected]

Shankar C. VenkataramaniUniversity of ArizonaDepartment of [email protected]

MS74

Pattern-Forming Fronts in Phyllotaxis

Some of the most spectacular patterns in the natural worldcan be found on members of the plant kingdom. Further-more, the regular configurations of organs on plants, col-lectively called phyllotaxis, exhibit a remarkable predispo-sition for Fibonacci and Fibonacci-like progressions. Start-ing from a biochemical and mechanical growth model simi-lar to the classic Swift-Hohenberg equation, we discuss theways in which nearly every property of phyllotaxis can beexplained as the propagation of a pushed pattern-forming

front.

Matthew PennybackerUniversity of [email protected]

MS74

Nanoscale Pattern Formation by Ion Bombardmentof Binary Compounds

When a solid surface is bombarded with a broad ion beam,a plethora of self-assembled nanoscale patterns can emerge,including nanodots arranged in hexagonal arrays of re-markable regularity. We discuss a theory that explains thegenesis of the strikingly regular hexagonal arrays of nan-odots that can form when binary materials are bombarded.In our theory, the coupling between a surface layer of al-tered stoichiometry and the topography of the surface is thekey to the observed pattern formation. We analyze how asoft mode related to the mean sputter yield can facilitatedefect formation and give rise to less ordered patterns.

Patrick ShipmanDepartment of MathematicsColorado State [email protected]

MS75

Relative Intensity Noise Transfer in Second-OrderRaman Amplification with Random DistributedFeedback Ultra-Long Fibre Lasers

The predicted RIN transfer function for second-order dis-tributed amplification based on different configurations ofRandom distributed feedback ultralong Raman fiber lasers(RDFLs) is found and studied over a broad range of pos-sible lengths and signal powers, showing that the values ofthe RIN transfer function and the RIN cut-off frequenciesare dependent upon both parameters. RIN performance iscompared to that of a typical cavity ultralong Raman fiberlaser pumped from the extremes.

Javier NunoInstituto de Optica, [email protected]

Juan Diego Ania Castanon

Instituto de ptica (CSIC), [email protected]

MS75

Transverse Disorder-Induced Localizations in Non-local Nonlinear Media: Theory and Experiments

We review our theoretical approach about the way localizedstates due to disorder are affected by the presence of non-linearity. We outline the link between Anderson localiza-tion and solitons, and study local and nonlocal responses.We also report on experimental results on two-dimensionaldisorder-induced localization in optical fibres, and the ob-servation of action at a distance and collective dynamicsinvolving localized states in nonlocal media.

Claudio ContiUniversita Sapienza, Rome, [email protected]

Viola Folli

122 NW14 Abstracts

Dep. Physics Sapienza Rome (IT)[email protected]

Marco LeonettiUniversity Sapienza, Rome, [email protected]

Salman Karbasi, Arash MafiUniversity of Wisconsin-Milwaukee, [email protected], [email protected]

MS75

Optical Wave Turbulence: Toward a Unified Non-Equilibrium Thermodynamic Description of Statis-tical Nonlinear Optics

We review a unified theoretical formulation of statisticalnonlinear optics on the basis of the wave turbulence theory,which provides a nonequilibrium thermodynamic descrip-tion of incoherent nonlinear waves. On the basis of thegeneralized NLS equation, we discuss the wave turbulencekinetic equation in analogy with kinetic gas theory, thelong-range Vlasov equation in analogy with Gravitationaldynamics, and the nonequilibrium description of nonin-stantaneous (Raman-like) nonlinearities in analogy withweak Langmuir turbulence in plasma.

Gang XuUniversity of BurgundyLaboratoire Interdisciplinaire Carnot de [email protected]

Josselin GarnierUniversity Paris DiderotLaboratoire de Probabilites et Modeles [email protected]

Stefano TrilloUniversity of [email protected]

Antonio PicozziUniversite’ de Bourgogne, Dijon, [email protected]

MS75

Order and Chaos in Fibre Lasers

We analyse the nonlinear stage of modulation instabilityin passively mode locked fiber lasers, leading to either sta-ble or chaotic or noise-like emission. We present the dia-gram of phase transitions among stable temporal patternsand different regimes of chaotic emission in terms of thekey cavity parameters such as dispersion and nonlinear-ity: amplitude or phase turbulence, and spatio-temporalintermittency. Whenever the polarizer is removed from thecavity, stabilization of the chaotic emission may occur viaspatio-temporal synchronisation induced by the nonlinearcoupling among two the orthogonal polarization modes.

Stefan WabnitzUniversity of Brescia

[email protected]

MS76

KP Web-solitons from Wave Patterns

Nonlinear interactions among small amplitude, long wave-length, obliquely propagating waves on the surface of shal-low water often generate web-like patterns. In this talk,we discuss how line-soliton solutions of the Kadomtsev-Petviashvili (KP) equation can approximate such web-pattern in shallow water wave. We describe an “inverseproblem” which maps a certain set of measurable data fromthe solitary waves in the given pattern to the parametersrequired to construct an exact KP soliton that describesthe non-stationary dynamics of the pattern. We illustratethe inverse problem using explicit examples of shallow wa-ter wave pattern.

Sarbarish ChakravartyUniversity of Coloradoat Colorado [email protected]

MS76

Invariant Manifold of the KdV Equation

The solution structure of the KdV equation is studied inlight of invariant manifold (IM). According to the defini-tion of IM, the first order IM of the KdV equation is ob-tained, which turns to describe the traveling wave solution. The relationship is recovered between the second ordergroup-invariant IM and the group-invariant solutions of theKdV. The concept of linear IM is presented to study thehigher order IM and the two sets of linear IMs concern-ing soliton and algebraic geometric solutions are investi-gated. The direct method for seeking the linear IM of agiven PDE system is presented and the existence of richlinear IMs is a strong indication that the given PDE is in-tegrable. We find that the first integrals of the reducedordinary differential equation can be obtained by the innersymmetry of the IMs. It is conjectured that the new (2+1)-dimensional differential-difference system is an integrablesystem including the well-known KdV reduction.

Yong ChenEastern China Normal [email protected]

Yuqi LiEastern China Normal [email protected]

Senyue LouNingbo University, [email protected]

MS76

General Solutions of Arbitraray First Order Au-tonomous PDEs

Using general symmetry approach, it is proved that ALLsolutions of arbitrary autonomous first order partial differ-ent equations (PDEs) can be obtained. In other words,a first order autonomous PDE in any dimensions is C-integrable. Especially, for arbitrary two dimensional firstorder autonoumous PDEs, the recursion operators, groupinvariant operators, Lax pairs, higer order general local and

NW14 Abstracts 123

nonlocal symmetries and group invariant functions are ex-plicitly given.

Senyue LouNingbo University, [email protected]

MS76

On Nonintegrable Semidiscrete Hirota Equation:Gauge Equivalent Structures and Dynamical Prop-erties

In this talk, we investigate nonintegrable semidiscrete Hi-rota equations including nonintegrable semidiscrete HirotaI equation and nonintegrable semidiscrete Hirota II equa-tion. We focus on the topics on gauge equivalent struc-tures and dynamical behaviours for the two nonintegrablesemidiscrete equations. By using the concept of the pre-scribed discrete curvature, we show that under the discretegauge transformations, nonintegrable semidiscrete Hirota Iand II equations are respectively gauge equivalent to thenonintegrable generalized semidiscrete modified Heisen-berg ferromagnet equation and the nonintegrable gener-alized semidiscrete Heisenberg ferromagnet equation. Weprove that the two discrete gauge transformations are re-versible. We study the dynamical properties for the twononintegrable semidiscrete Hirota equations. The exactspatial period solutions of the two nonintegrable semidis-crete Hirota equations are obtained through the construc-tions of period orbits of the stationary discrete Hirota equa-tions. We discuss the topic that the spatial period prop-erty of the solution to nonintegrable semidiscrete Hirotaequation is whether preserved to that of the correspond-ing gauge equivalent nonintegrable semidiscrete equationsor not under the action of discrete gauge transformation.We also give the numerical simulations for the stationarydiscrete Hirota equations. We find that their dynamics aremuch richer than the ones of stationary discrete nonlinearSchrodinger equations. This is a joint work with Li-yuanMa.

Zuonong ZhuDepartment of Mathematics,Shanghai Jiaotong University, [email protected]

MS77

Mobile Localized Solutions for An Electron in Lat-tices with Dispersive and Non-Dispersive Phonons

We consider a one dimensional lattice in which an electroncan interact both with on-site nondispersive (Einstein)phonons and with longitudinal dispersive acoustic (Debye)phonons and provide existence conditions for mobile local-ized electron excitations in the long wave limit. The role ofboth types of phonon modes on localization is also assessed,together with a discussion of differences existing betweenthe discrete and the continuum approaches. A striking re-sult is that, under certain conditions localized states canonly be stable if they have a non-zero velocity.

Luis CisnerosESFM, Instituto Politecnico [email protected]

MS77

Surface Signature of Internal Waves

Based on a Hamiltonian formulation of a two-layer ocean,

we derive an asymptotic model for surface-internal waveinteractions, where the nonlinear internal waves evolve ac-cording to a KdV equation, while the smaller-amplitudesurface waves are described by a linear Schrodinger equa-tion. For internal solitons of depression, the Schrodingerequation is shown to be in the semi-classical regime andthus admits localized bound states. This leads to the phe-nomenon of trapped surface modes which propagate as thesignature of the internal waves. Numerical simulations tak-ing oceanic parameters into account are performed to il-lustrate this phenomenon. This is joint work with WalterCraig and Catherine Sulem.

Philippe GuyenneDepartment of Mathematical SciencesUniversity of [email protected]

MS77

Dynamics of Localized Solution in Nonlocal NLSEquation with Double Well Potential

In this talk, we examine the combined effects of cubic andquintic terms of the long range type in the dynamics of adouble well potential. Employing a two-mode approxima-tion, we systematically develop two cubic-quintic ordinarydifferential equations and assess the contributions of thelong-range interactions in each of the relevant prefactors,gauging how to simplify the ensuing dynamical system. Fi-nally, we obtain a reduced canonical description for theconjugate variables of relative population imbalance andrelative phase between the two wells and proceed to a dy-namical systems analysis of the resulting pair of ordinarydifferential equations. The relevant bifurcations, the sta-bility of the branches and their dynamical implications areexamined both in the reduced (ODE) and in the full (PDE)setting.

Vassilis M. RothosAristotle University of [email protected]

MS77

The Role of Radiation Loss in the Evolution of El-liptic Solitons in Nonlocal Soft Media

Optical solitary waves can propagate in a nematic liquidcrystal, which exhibits an intensity dependent refractive in-dex change, balancing beam diffraction and self-focusing.The evolution of an elliptical nematicon with orbital an-gular momentum is investigated. Modulation theory andnumerical solutions show that shed diffractive radiation iscritical to this evolution, which occurs in two phases. First,angular momentum is shed via spiral waves, reshaping thebeam. Secondly, diffractive radiation loss drives the beamtowards its steady state.

Luke SciberrasUniversidad Nacional Autonoma de [email protected]

MS78

Waves on the Interface of Two-Layer Liquid SystemSubject to Longitudinal Vibrations: Stability andCollision of Solitons

We consider dynamics of the internal interface in two-layerliquid system subject to longitudinal vibrations. We derivethe equations of average dynamics of large-scale patterns

124 NW14 Abstracts

on the interface, reveal a one-parametric family of solitonsand show that the persisting system dynamics is merelythe kinetics of a set of these solitons. Collisions of solitonsare comprehensively studied. Class of collisions leading toexplosive layer rupture is revealed; formation of the ruptureis both observed numerically and described analytically.

Denis S. GoldobinInstitute for Physics, University of PotsdamPotsdam, [email protected]

Kseniya KovalevskayaTheoretical Physics DepartmentPerm State Universityk [email protected]

MS78

Coherent Structures Interaction and Self-Organization in Dissipative Turbulence

We study interactions of coherent structures in a fallingfilm as a generic prototype of dissipative turbulence. Ouranalysis is based on a low-dimensional formulation and di-rect numerical simulations (DNS). A rich and complex dy-namics is observed, with monotonic, underdamped or self-sustained oscillations, finding excellent DNS-theory agree-ment. We also consider a shear-thinning falling film thatyields hysteresis on the coherent structures as the Reynoldsnumber increases which we quantify with appropriate sta-bility analysis.

Serafim KalliadasisDepartment of Chemical EngineeringImperial College [email protected]

Marc PradasDepartment of Mathematical [email protected]

Te-Sheng LinDepartment of Mathematical SciencesLoughborough [email protected]

Dmitri TseluikoDepartment of Mathematical [email protected]

MS78

Modulation of a Heat Flux in a Layer of BinaryMixture

We consider nonlinear dynamics of a longwave Marangoniconvection in a binary liquid layer subject to a modulatedheat flux at the bottom. It is shown that nonlinear evolu-tion for synchronous and subharmonic modes is governedby the same set of standard Landau equations with the co-efficients calculated numerically. For both modes the tran-sition to the case of no modulation is nontrivial and thecorresponding intermediate asymptotics are developed.

Irina FayzrakhmanovaDepartment of General PhysicsPerm State Technical University, Perm, [email protected]

Sergey ShklyaevInstitute of Continuous Media MechanicsPerm, [email protected]

Alexander NepomnyashchyTechnionIsrael Institute of [email protected]

MS78

Symmetries and Parametric Instabilities in Vibrat-ing Containers

Symmetries, either exact or approximate, play an essentialrole in pattern forming systems, in particular under oscil-latory excitation, suppressing some of the resonances ex-pected in the generic case and enhancing others. This willbe illustrated considering parametric excitation of surfacewaves in finite containers in several distinguished regimes,including single-mode and modulated patterns, horizontaland vertical excitation, and various excitation mechanismssuch as vibration of the whole container and immersedwave makers.

Jose Manuel VegaUniversidad Politecnica de [email protected]

MS79

Model Reduction for Waves in Networks

The propagation of localized waves in nonlinear networksis an ubiquitous problem. Examples are fluxon motion inarrays of Josephson junctions, pulse propagation in the cir-culatory system. Modeling such problems is difficult andit is helpful to simplify the equation and the geometry. Wewill illustrate these issues with the analysis of the propa-gation of sine-Gordon waves through Y junctions.

Jean-Guy CaputoINSA de [email protected]

MS79

Partial Continuum Limits for Exciton Pulses inLarge Molecules

Numerical solutions of ODEs related to the discrete NLSequation often develop propagating pulses with slow spatialvariation, which has motivated the search for approxima-tions by PDEs. In this talk, it is observed that these pat-terns are substantially different from previously-consideredNLS approximations, and several new PDE approxima-tions are presented: systems related to the Airy PDE, anda quite different system describing oscillations near end-points. Numerical solutions and linear analysis show goodagreement with the long-wave phenomena in the ODEs.

Brenton J. LeMesurierCollege of CharlestonDepartment of Mathematics

NW14 Abstracts 125

[email protected]

MS79

Disorder in One-Dimensional Granular Crystals

We study the effects of multiple types of disorder —both correlated and uncorrelated — and nonlinearities onthe evolution of an initially localized excitation in a one-dimensional granular crystal. In the linear limit, we exam-ine various regimes of subdiffusivity, superdiffusivity, andabsence of diffusion. These regimes depend on the strengthand type of disorder as well as on the normal modes of thelinear spectrum. When we introduce nonlinearity, we ob-serve a gradual delocalization.

Alejandro J. MartinezMathematical InstituteUniversity of [email protected]

MS79

Model Reduction in Optics and Traffic Modeling

This talk introduces some recurring ideas and methods inmodel reduction by describing two apparently diverse prob-lems where similar reduction techniques are useful and re-lated wave phenomena arise. The first is the Zeno effect forsoliton type pulses in a nonlinear directional coupler withdissipation. The effect consists in increase of the couplertransparency with increase of the dissipative losses in oneof the arms (joint work with F. Abdullaev et al). The sec-ond is traffic modeling, and methods for reducing trafficjams through modulations of parameters, such as stochas-tic modulation of the safety distance (joint work with YuriGaididei et al).

Mads SørensenDepartment of Applied Mathematics and ComputerScienceTechnical University of [email protected]

MS80

Sloshing Dynamics with the Hamiltonian Particle-mesh Method

The Hamiltonian Particle-Mesh (HPM) method of [J.Frank, G. Gottwald & S. Reich. A Hamiltonianparticle-mesh method for the rotating shallow-water equa-tions, Meshfree Methods for Partial Differential Equa-tions,Lecture Notes in Computational Science and Engi-neering, Springer 26 131142 (2002).] is used to developa symplectic integrator in Eulerian-Lagrangian coordinatesystems for the problem of dynamic coupling betweenshallow-water sloshing and horizontal vehicle motion. Asimple and fast numerical algorithm with excellent energyconservation over long times, based on the Stormer-Verletmethod is implemented. Numerical simulations of the cou-pled dynamics are presented and compared to the resultsof [H. Alemi Ardakani & T.J. Bridges. Dynamic couplingbetween shallow-water sloshing and horizontal vehicle mo-tion, European Journal of Applied Mathematics 21 479517(2010).] where the coupled fluid-vehicle problem is anal-ysed in the pure Lagrangian Particle-Path (LPP) setting.

Hamid Alemi ArdakaniDepartment of MathematicsUniversity of Surrey

[email protected]


Matthew R. TurnerUniversity of [email protected]

MS80

Transversality of Solitary Waves and Their Stabil-ity

Variationnal partial differential equations like the Swift-Hohenberg equation or the Kawahara equation have anHamiltonian steady part. This steady part can have an ho-moclinic tangle, a phenomenon which implies the existenceof an infinity of isolated waves or solitary waves for thePDE. In this talk, we will describe how the Lazutkin invari-ant, a quantity originally introduced to study the steadypart, can be related to the stability problem.

Frederic ChardardUniversite Jean Monnet/Institut Camille [email protected]

MS80

An Application of Maslov Index to the StabilityAnalysis for Standing Pulses

For the FitzHugh-Nagumo equations, a standing pulse so-lution is a homoclinic orbit of a second order Hamiltoniansystem. We employ the Maslov index theory to give certaincriteria for the stability of standing pulse. Related resultsare also applicable to more general skew-gradient systems.

Chiao-Nen ChenDepartment of mathematicsNational Changhua University of Education, Taiwan,[email protected]

MS80

Stability of Periodic Waves in Hamiltonian Pdes

Many partial differential equations endowed with a Hamil-tonian structure are known to admit rich families of peri-odic traveling waves. The stability theory for these wavesis by many respects still in its infancy though. The mainpurpose of this talk is to point out a few results, for KdV-like equations and systems, that make the connection be-tween three kind of approaches: spectral, variational, andmodulational.

Miguel RodriguesUniversity of [email protected]

MS81

Experimental Observation of Unstable Mode 2 In-ternal Waves

The structure and stability of mode 2 internal solitary-likewaves were investigated. The amplitude of the wave and

126 NW14 Abstracts

the offset of the pycnocline (with regard to the mid-depthof the water) were varied. In non-zero offset cases, it wasfound that the critical amplitude required for instabilitywas less than in the zero offset counterpart case. It wasalso found that increasing the offset value led to increasesin the asymmetry of the wave.

Magda CarrSchool of Mathematics and StatisticsUniversity of St Andrews, [email protected]

Peter A DaviesDepartment of Civil EngineeringUniversity of Dundee, [email protected]

Ruud HoebersDepartment of Applied PhysicsEindhoven University of Technology, [email protected]

MS81

Hydraulic Falls Under a Floating Ice Plate

Steady two-dimensional nonlinear flexural-gravity hy-draulic falls past a submerged obstruction on the channelbottom are considered. The fluid is assumed to be idealand is covered above by a thin ice plate. Cosserat the-ory is used to model the ice plate as a thin elastic shell,and boundary integral equation techniques are employedto find critical flow solutions. By utilising a second ob-struction, solutions with a train of waves trapped betweenthe obstructions are investigated.

Charlotte PageSchool of Computing SciencesUniversity of East Anglia, Norwich, [email protected]

Emilian I. ParauUniversity of East [email protected]

MS81

Analysis and Computations of the Initial ValueProblem for Hydroelastic Waves

First, we summarize a new existence and uniqueness prooffor the initial value problem for hydroelastic waves in 2Dflow. The proof uses energy methods, following earlier workby Ambrose on vortex sheets with surface tension. Sec-ond, an efficient, nonstiff boundary integral method for 3Dhydroelastic waves is presented. The stiffness is removedby developing a small-scale decomposition, in the spirit ofprior work on 2D vortex sheets with surface tension byHou, Lowengrub and Shelley. The existence theory andnumerical method both rely on a formulation of the prob-lem using a generalized isothermal parameterization of theinterface. This is joint work with David Ambrose.

Michael SiegelNew Jersey Institute of [email protected]

MS81

Comparing Stokes Drift for Internal and Surface

Gravity Wave Packets

We compare and contrast existing and new results for theStokes drift and associated return flow for surface gravitywave packets on an unstratified fluid to new results for theStokes drift and its “return flow’ for Boussinesq internalgravity wave packets on a linearly stratified fluid. We doso by exploring a perturbation expansion in two small pa-rameters, the steepness and the bandwidth of the packet,and provide a numerical validation.

Ton van den Bremer, Paul TaylorUniversity of [email protected],[email protected]

Bruce SutherlandUniversity of [email protected]

MS82

Stablility of Localized Structure for a Semi-AridClimate Model

This talk will give a brief overview of dynamical systemsand climate. We will also detail recent stability resultsand multi-pulse interaction laws for N-pulse semi-strongsolutions to the Gray-Scott model. This model has recentlybeen used to describe vegetative pattern formation in asemi-arid ecosystem.

Thomas BellskyArizona State [email protected]

MS82

Model Reduction and Response for Two-TimescaleSystems Using Fluctuation-Dissipation

Direct numerical simulation of a large multiscale system istypically cost prohibitive. We present a method to gener-ate reduced models for the slow variables of two-timescaleODE systems using an averaging method combined withthe fluctuation-dissipation theorem to obtain a linear re-sponse correction term for the averaged fast dynamics. Weapply this method to a two-scale Lorenz ’96 model andanalyze the statistics and perturbation response of the re-sulting reduced system.

Marc KjerlandUniversity of Illinois at [email protected]

MS82

Tipping and Warning Signs for Patterns and Prop-agation Failure in SPDEs

In this talk, I shall report on recent results on early- warn-ing signs for pattern formation in stochastic partial dif-ferential equations. In particular, it will be shown thatclassical scaling laws from stochastic ordinary differentialequations can be carried over to the SPDE case. This isillustrated in the context of the Swift- Hohenberg equa-tion, analytically and numerically. Furthermore, I shalldiscuss numerical results for warning signs for the stochas-tic Fisher- KPP equation in the case of noisy invasion fronttravelling waves near positive absorption probability events

NW14 Abstracts 127

leading to propagation failure.

Karna V. GowdaNorthwestern [email protected]

Christian KuehnVienna University of [email protected]

MS82

Semi-Strong Desertification Dynamics with aSlowly Changing Parameter

We introduce a slowly changing parameter in the frame-work of semi-strong interaction of pulses in reaction dif-fusion systems, which appear as models for vegetationin (semi-)arid regions. Geometric singular perturbationtheory yields laws of motion for the pulses and spectral(in)stability of the configuration. Crucial is understand-ing the interplay between the inherent slow dynamics ofthe pulse interactions and the rate of change of the chang-ing parameter: will ecosystem response be fast enough topostpone destabilization by a changing parameter?

Eric SieroLeiden University, Mathematical [email protected]


Thomas BellskyArizona State [email protected]

MS83

Thermo-Optical Effects and Mode Instabilities inLarge Mode Area Photonic Crystal Fibers

In recent years fiber laser systems have shown a rapid evo-lution in terms of beam quality and power. High pulseenergies and peak power require large effective area andnew photonic crystal fiber designs are proposed. Thermo-optical effects can lead to transverse mode instability(TMI), a nonlinear effect that sets in at a threshold powerlevel. The numerical models of TMI for understanding theorigin and mechanism behind, and for future mitigationstrategies are discussed.

Annamaria CucinottaUniversita degli Studi di Parma, Parma, [email protected]

Enrico Coscelli, Federica Poli, Stefano SelleriUniversity of Parma, Parma, [email protected], [email protected], [email protected]

MS83

Tuning of Surface Plasmon Polaritons Beat Lengthin Graphene Directional Couplers

We investigate the tuning of the coupling of surface plas-mon polaritons between two spatially separated graphenelayers. We demonstrate that the coupling coefficient insuch structures can be easily controlled by means of an

applied electrical signal. We prove theoretically and nu-merically that by slightly changing the chemical potential,a graphene coupler can switch from the bar to the crossstate.

Costantino De AngelisUniversity of Brescia, Brescia, [email protected]

Aldo Auditore, Andrea LocatelliUniversity of [email protected], [email protected]


MS83

Self-Tuning Nonlinear Optical Systems

We demonstrate that the integration of data-driven ma-chine learning strategies with adaptive control produce anefficient and optimal self-tuning algorithm for mode-lockedfiber lasers. The adaptive controller is capable of obtain-ing and maintaining high-energy, single-pulse states in amode-locked fiber laser while the machine learning char-acterizes the cavity itself for rapid state identification andimproved optimization. The theory developed is demon-strated on a nonlinear polarization rotation (NPR) basedlaser using waveplate and polarizer angles to achieve opti-mal passive mode-locking despite large disturbances to thesystem. The physically realizable objective function intro-duced divides the energy output by the fourth moment ofthe pulse spectrum, thus balancing the total energy withthe time duration of the mode-locked solution. The meth-ods demonstrated can be implemented broadly to opticalsystems, or more generally to any self-tuning complex sys-tems.

J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]

Steven Bruton, Xing FuApplied MathematicsUniversity of [email protected], [email protected]

MS83

Ultrafast Spatial and Temporal Soliton Dynamicsin Gas-Filled Hollow-Core Photonic Crystal Fibres

Optical solitons form the core of the many of the most ex-citing nonlinear phenomena in nonlinear fibre optics forexample, they are the basis of a plethora of supercontin-uum mechanisms. Next generation photonic-crystal fibresfilled with gas provide new opportunities and regimes to ex-plore soliton physics, ranging from the influence of soliton-induced plasma, to the possibility of guiding and generat-ing sub-cycle and vacuum-UV optical fields. A range oftheoretical and experimental results will be discussed.

John Travers, Francesco Tani, Ka Fai Mak, PhilippHolzer, Alexey Ermolov, Philip RussellMax Planck Institute for the Science of Light, Erlangen,[email protected], [email protected],[email protected], [email protected],

128 NW14 Abstracts


MS84

Standing Waves and Heteroclinic Networks in theNonlocal Complex Ginzburg-Landau Equation forElectrochemical Systems

The nonlocal complex Ginzburg-Landau equation [V.Garcia-Morales and K. Krischer, Phys. Rev. Lett. 100,054101 (2008)] describes the interaction between the elec-trostatic potential and the oscillatory nonlinear kineticsof spatially extended electrochemical systems. This equa-tion is shown to exhibit heteroclinic netwroks and standingwaves (under global coupling). The latter lead to complexinterference patterns, with active subharmonic modes. Lin-ear stability and symmetry analysis allow detailed featuresof these coherent structures to be elucidated.

Vladimir Garcia-MoralesDepartment of PhysicsTechnische Universitat [email protected]

MS84

Bifurcations in the Langmuir-Blodgett TransferProblem

Spontaneous pattern formation in deposition processes atreceding contact lines has become a versatile tool to coatsubstrates with well controlled micro- and nanostructures.As a paradigmatic example, the coating of substrates withperiodically structured monolayers has in recent years beeninvestigated by theoreticians and experimentalists [Kopf etal, New J. Phys. 14 (2012) 02316 and Langmuir 26 (2010)10444, Li et al, Small 8 (2012) 488] alike. Here, we presentrecent progress, allowing for the first time to understandthe intricate bifurcation diagram of the system that ex-hibits a snaking branch of stationary solutions. Each noseof the snake is connected to a branch of time periodic so-lutions. Using numerical continuation, we detect variouslocal and global bifurcations and investigate how the solu-tion structure depends on the system size. These resultsare of wide interest for the theoretical description of pat-tern formation in systems with nontrivial boundary condi-tions.

Michael H. KoepfDepartement de PhysiqueEcole Normale [email protected]

Uwe ThieleInstitute of Theoretical PhysicsUniversity of [email protected]

MS84

Coherent Structures in Confined Swarming Flows

Swarming flows display new interesting behaviours as-sociated with the collective dynamics of interacting ac-tive swimmers. We report new observations of collectivemotion of concentrated semen arising inside an annulusthrough spontaneous symmetry breaking. The resultingself-sustained dynamics shows various interesting regimessuch as constant rotation, oscillating rotation, and dampedoscillations. A similar configuration is analyzed through alinear instability analysis of the Viksek model which dis-

play a rich variety of modes with similar behaviour.

Franck [email protected]

Adama Creppy, Olivier PraudToulouse University, IMFT UMR 5502, 31400 [email protected], [email protected]

Pierre DegondImperial College of London, Applied mathematics [email protected]

Hui YuUniversite de Toulouse; UPS, INSA, UT1, UTM ;[email protected]

Nan WangNational University of Singapore, Department [email protected]

MS84

On Electrical Diffuse Layers in Ionic Liquids andHeteroclinic-Type Connections

Studies of room temperature ionic liquids, showed thatelectrical diffuse layers can be thick and exhibit spatiallyextended non-monotonic (oscillatory) and monotonic de-cays. These unconventional properties are fundamentallydifferent from traditional (dilute) electrolytes and demon-strate the limited mechanistic understanding of highly con-centrated electrolytes. To advance the understanding ofelectrical diffuse layers in ionic liquids we use a semi-phenomenological modified Poisson-Nernst-Planck equa-tions and regulate weak dilutions. Using spatial dynamicsand numerical methods, we analyze distinct diffuse layercharacteristics and provide for each type the analytic con-ditions and the validity limits in terms of applied voltage,domain size, molecular packing, and short range electro-static correlations. We also discuss the qualitative general-ity of the results via global heteroclinic-type connections.

Arik YochelisDepartment of Chemical EngineeringTechnion - Israel Institute of [email protected]

MS85

Controlability of Schroedinger Equation with aHartree Type Nonlinearity

We are concerned with the control problem for

i ut = −uxx + α(x)u+

(∫(|x− y| − |x|)|u(y, t)|2dy

)u,

where the Hartree nonlinearity stems from the couplingwith the 1D Poisson equation, and α(x) ∈ C∞ has lineargrowth at infinity, including constant electric fields. Weshall show that for both small initial and target states,and for distributed controls supported outside of a fixedcompact interval, the model equation is controllable. Weshall also give non controllability results for distributedcontrols with compact support

Mariano De Leo

NW14 Abstracts 129

Universidad Nacional General [email protected]

MS85

Exact and Approximate Solutions for SolitaryWaves in Nematic Liquid Crystals

The system described solitary waves in nematic liquidcrystals (NLC) is general, arising in many other areas ofphysics.. Isolated exact solutions and general variationalapproximations are found for solitary waves in NLC’s.These approximate solutions are compared with numericalsolutions and the relative merits of different ansatze arediscussed. Physically, we find a type of bistability in thesystem and a minimum power for solitary waves to exist.

Michael MacNeilUniversity of [email protected]

MS85

Localized Solutions and Traveling Waves ina Nonlocal Parametrically Forced NonlinearSchroedinger Equation

The parametrically forced nonlinear Schroedinger equationis a model for nonlinear dissipative systems, including de-tuned operation of optical parametric oscillators. It hasbeen shown to support a rich variety of localized solu-tions, including standing, periodic and (unstable) travel-ing waves. We show how coupling this equation to a heatequation produces stable traveling waves whose dynamicscan be understood through a simple reduction to collectivecoordinates, and we discuss their connection to solutionsof the uncoupled equation.

Richard O. MooreNew Jersey Institute of [email protected]

MS86

Continuously Quenched Pattern Dynamics in Dry-ing Liquid Films

The nonlinear dynamics of Bnard-like surface-tension-driven patterns in thin liquid films evaporating into am-bient air is analyzed experimentally and theoretically. Dueto the layer thickness decrease, the average size of convec-tion cells continuously decreases by a fast mitosis process,which results in highly disordered structures. Their char-acteristics are studied using a long-wave convection model,which compares qualitatively well with experiments. Asimple fitting-parameter-free model is also proposed for thethreshold thickness below which patterns disappear.

Pierre ColinetService de Chimie Physique E.P.Universite Libre de Bruxelles, Brussels, [email protected]

MS86

Wave Instability of a Rotating Liquid-Liquid Inter-face

Experimental study is performed of rotating system of twoimmiscible liquids of different density. Inertial waves, ex-cited on the centrifuged interface under external periodic

force action perpendicular to rotation axis, are consid-ered. Excitation of interface differential rotation is ob-served. With an increase of external forcing, an azimuthalwave, characterized by pronounced two-dimensional crestsparallel to rotation axis, is excited on the interface accom-panied with interface differential rotation velocity increase.Thresholds of interface stability are studied.

Nikolay KozlovDepartment of General and Experimental PhysicsPerm State Pedagogical University, Perm, [email protected]

Anastasiia Kozlova, Darya ShuvalovaLaboratory of Vibrational HydromechanicsPerm State Humanitarian Pedagogical University, Perm,[email protected], [email protected]

MS86

Thin Film Flows over Spinning Discs: NumericalSimulation of Three-Dimensional Waves

We model the flow of a thin film over a rotating disc us-ing the integral method coupled to the method of weightedresiduals to derive a set of evolution equations for the in-terface, and the radial and azimuthal flow rates. Theseequations account for centrifugal, inertial, and capillaryforces and the transition from two-dimensional to three-dimensional waves as these waves travel towards the discperiphery. We compare our results with those from fullNavier-Stokes simulations.

Omar K. MatarImperial College [email protected]

MS86

Compactons Induced by Nonconvex Advection

Using the model equation ut ± (u3 − u2)x + (u3)xxx = 0we study the impact of a non-convex convection on forma-tion of compactons. In the ositive version, both travelingand stationary compactons are observed, whereas in thenegative branch, compactons may form only for a boundedrange of velocities. Depending on their relative speed, in-teraction of compactons may be close to being elastic or afission process wherein the collision gives rise to additionalcompactons.

Alex OronDepartment of Mechanical EngineeringTechnion - Israel Institute of Technology, Haifa, [email protected]

Philip RosenauTel Aviv [email protected]

MS87

Settling and Rising in Density Stratified Fluids:Analysis and Experiments


Roberto CamassaUniversity of North Carolina

130 NW14 Abstracts

[email protected]

MS87

Transcritical Flow of a Stratified Fluid Over Topog-raphy and Non-classical Dispersive Shock Waves

We study transcritical flow of a stratified fluid past a broadlocalised topographic obstacle using the recent develop-ment of the nonlinear modulation theory for the forcedGardner equation. We identify some of the wave struc-tures generated by the transcritical flow as dispersive coun-terparts of non-classical shocks and double waves occurringin the regularisation of non-convex hyperbolic conservationlaws. The talk is based on joint works with R. Grimshaw,A. Kamchatnov and M. Hoefer.

Gennady ElLoughborough University, United [email protected]

MS87

Solute Dynamics Within Settling Marine Snow atDensity Discontinuities


Morten IversenMarum - Geophysical SciencesBremen [email protected]

MS87

Experiments and Theory for Porous Spheres Set-tling in Sharply Stratified Fluids

Marine snow, aggregates composed of organic and inor-ganic matter, play a major role in the carbon cycle. Mostof these particles are extremely porous, allowing diffusionof a stratifying agent from the ambient fluid to affect thedensity and therefore the settling dynamics. We study thecase of a single spherical particle settling in water strati-fied by salt, focusing on effects of porosity and diffusion. Aparametric study of the settling behaviors and comparisonsbetween modeling and experiments will be presented.

Shilpa KhatriDepartment of MathematicsUniversity of North Carolina at Chapel [email protected]


Richard McLaughlinUNC Chapel [email protected]

Jennifer PrairieUniversity of North Carolina at Chapel [email protected]

Brian WhiteUniversity of North [email protected]

Sungduk YuUniversity of North Carolina at Chapel Hill

[email protected]

MS88

Multisymplectic Structure and the Stability of Soli-tary Waves

A challenge in the stability analysis of solitary waves is tofind general conditions for stability or instability. In thistalk it is shown how multi-symplectic structures leads toa general instability condition for a large class of solitarywaves of Hamiltonian PDEs. It generalizes theory of Pego& Weinstein (1992) and Bridges & Derks (2001), and usesnew results of Bridges & Chardard (2014) on transversality.It is shown that the product of the the Lazutkin-Treschevinvariant, and dI/dc, the derivative of the momentum withrespect to the speed, generates a sufficient condition forlinear instability of solitary waves.


MS88

Standing Pulse Solution of Fitzhugh-NagumoEquations

Using a variational formulation, we study standing pulsesolutions of the FitzHugh-Nagumo equations when the ac-tivator diffusion coefficient is small compared to that ofthe inhibitor. There is no global minimizer in this case, wetherefore look for local minimizer by imposing appropriatetopological constraints on the solution space. Interestingtechniques are developed to deal with such classes of topo-logical constraints.

Yung-Sze ChoiUniversity of [email protected]

MS88

Dispersive Shear Shallow Water Flows

We derive a new dispersive model of shear shallow waterflows through the Hamilton principle. The model general-izes the well-known Green-Naghdi model.

Sergey GavrilyukUniversity Aix-Marseille, UMR CNRS 6595 [email protected]

MS88

A Hamiltonian Analogue of the Meandering Tran-sition

A Hamiltonian analogue of the meandering transition fromrotating waves to modulated traveling waves (TWs) in sys-tems with Euclidean symmetry is presented. In dissipativesystems this transition is associated with a Hopf bifurca-tion. In the Hamiltonian case, for example in models ofpoint vortex dynamics, the conserved quantities of the sys-tem are bifurcation parameters. Depending on symme-try, it is shown that either modulated TWs do not occur,or modulated TWs are the typical scenario near rotatingwaves.

Claudia WulffUniversity of SurreyDept. of Math and Statistics

NW14 Abstracts 131

[email protected]

MS89

Axisymmetric Solitary Waves on a Ferrofluid Jet

The propagation of axisymmetric solitary waves on thesurface of a cylindrical ferrofluid jet subjected to a mag-netic field is investigated. A numerical method is used tocompute fully-nonlinear travelling solitary waves and pre-dictions of elevation waves and depression waves by Ran-nacher & Engel (2006) using a weakly-nonlinear theory areconfirmed in the appropriate ranges of the magnetic Bondnumber. New nonlinear branches of solitary wave solutionsare identified. As the Bond number is varied, the solitarywave profiles may approach a limiting configuration witha trapped toroidal-shaped bubble, or they may approach astatic wave if the wave speed approaches zero. For a suf-ficiently large axial rod, the limiting profile may exhibit acusp.

Mark BlythSchool of MathematicsUniversity of East Anglia, Norwich, [email protected]

MS89

On the Interaction Between Surface and InternalWaves

We consider a system of two fluids of different densitiesbounded above by a free surface. The propagation of sur-face and internal waves generated by an external forcingand their interaction are studied both theoretically andexperimentally.

Wooyoung ChoiDept of MathematicsNew Jersey Institute of [email protected]

MS89

Computing the Pressure in Fully Nonlinear Long-Wave Models for Surface Water Waves

The effect of a linear background shear flow on the pres-sure beneath steady long gravity waves at the surface ofa fluid is investigated. Using an asymptotic expansion forthe streamfunction, we derive a model equation given interms of the background vorticity, the volume flux, thetotal head and the momentum flux. It is shown that astrongly sheared flow leads to nonmonotonicity of the fluidpressure in the sense that the maximum pressure is not lo-cated under the wave crest, and the pressure just beneaththe wavecrest can be below atmospheric pressure.

Henrik KalischUniversity of [email protected]

MS89

Davies Approximation of Levi-Civita’s SurfaceCondition for Water Waves in the Complex Do-main

Levi-Civita’s surface condition is the free surface conditionfor an irrotational plane flow using the logarithmic hodo-graph variable. This condition allows us to apply Davies’approximation to the problem of steady water waves, and

discuss all waves, from small-amplitude waves to the high-est one with a corner flow at the crest. This work inves-tigates singularity structure of this approximate solution,and compares the high-order Davies approximations withsome other standard methods including long wave approx-imation.

Sunao MurashigeFaculty of Systems Information ScienceFuture University [email protected]

Wooyoung ChoiDept of MathematicsNew Jersey Institute of [email protected]

MS90

Automatic Recognition and Tagging of Topologi-cally Different Regimes in Dynamical Systems

We discuss robust methods to characterize and detectsudden shifts, eg. critical transitions, between differentregimes in stochastic dynamical systems, with examplesfrom classical dynamics as well as real world climatologi-cal data. We develop techniques for the detection of suchcritical transitions from sparse observations contaminatedby noise. We present a machine learning framework whichaccurately tags different regimes of a dynamical systemsbased on topologically persistent features near an attrac-tor. In particular, our methodology performs well in thecontext of periodic orbits and saddle-type bifurcations.

Jesse BerwaldInstitute for Mathematics and its ApplicatonsUniversity of [email protected]

MS90

Data Assimilation for Quadratic Dissipative Dy-namical Systems

Data assimilation refers to the incorporation of a model of asystem together with data in the form of noisy observationsof that system in order to infer the underlying state and/orparameters of the system. In the case in which the data isreceived online and incorporated sequentially, it is referredto as filtering. We present accuracy and well-posednessresults for two prototypical filters, 3DVAR and EnKF, fora broad class of quadratic dissipative dynamical systems,including Navier-Stokes, Lorenz ’96, and Lorenz ’63.

Kody LawSRI UQ Center, CEMSE, [email protected]

MS90

Mixed Mode Oscillations in Conceptual ClimateModels: An In-depth Discussion

This talk analyzes a fast/slow system with one fast and twoslow variables. Geometric singular perturbation theory isused to demonstrate the existence of a folded node singu-larity. A parameter regime is found in which the foldednode leads to a stable MMO orbit through a generalizedcanard phenomenon.

Andrew RobertsDepartment of Mathematics

132 NW14 Abstracts

The University of North Carolina at Chapel [email protected]

Esther WidiasihDepartment of MathematicsThe University of [email protected]

Chris JonesUniversity of North Carolina-Chapel [email protected]

Martin WechselbergerUniversity of [email protected]

MS90

Mixed Mode Oscillations in Conceptual ClimateModels: A General Perspective

Much work has been done on relaxation oscillations andother simple oscillators in conceptual climate models. Theoscillatory patterns frequently found in climate data how-ever are often more complicated than what can be de-scribed by such mechanisms. In this talk, I will presentsome recent work incorporating ideas from the study ofmixed mode oscillations into conceptual modeling of cli-mate systems.

Esther WidiasihDepartment of MathematicsThe University of [email protected]

MS91

The Nonlocal Nonlinear Wave Equation with Peri-odic Boundary Conditions: Analytical and Numer-ical Results

We consider a general class of nonlinear nonlocal waveequation arising in one-dimensional nonlocal elasticity [N.Duruk, H. A. Erbay, A. Erkip, ”Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems aris-ing in elasticity”, Nonlinearity, 23, 107-118, (2010)]. Themodel involves a convolution operator with a general ker-nel function whose Fourier transform is nonnegative. Wefocus on well-posedness and blow-up results for the nonlo-cal wave equation with periodic boundary conditions. Wethen propose a Fourier pseudo-spectral numerical method.To understand the structural properties of the solutions,we present some numerical results illustrating the effectsof both the smoothness of the kernel function and thestrength of the nonlinear term on the solutions. This workhas been supported by the Scientific and Technological Re-search Council of Turkey (TUBITAK) under the projectMFAG-113F114.

Handan BorlukDepartment of Mathematics, Isik [email protected]

Gulcin M. MusluDepartment of Mathematics, Istanbul TechnicalUniversity

[email protected]

MS91

Orbital Stability of Solitary Waves of ModerateAmplitude in Shallow Water

We study the orbital stability of solitary traveling wavesolutions of the following equation for surface water wavesof moderate amplitude in the shallow water regime:

ut+ux+6uux−6u2ux+12u3ux+uxxx−uxxt+14uuxxx+28uxuxx = 0.

Our approach is based on a method proposed by Grillakis,Shatah and Strauss in 1987, and relies on a reformulationof the evolution equation in Hamiltonian form. We deducestability of solitary waves by proving the convexity of ascalar function, which is based on two nonlinear functionalsthat are preserved under the flow.

Nilay Duruk MutlubasIstanbul Kemerburgaz [email protected]


MS91

Local Well-posedness for a Class of Nonlocal Evo-lution Equations of Whitham Type

For a class of pseudodifferential evolution equations of theform

ut + (n(u) + Lu)x = 0,

we prove local well-posedness for initial data in the Sobolevspace Hs, s > 3/2. Here L is a linear Fourier multi-plier with a real, even and bounded symbol m, and n isa real measurable function with n′′ ∈ Hs

loc(R), s > 3/2.The proof, which combines Kato’s approach to quasilinearequations with recent results for Nemytskii operators ongeneral function spaces, applies equally well to the solitaryand periodic cases.

Mats EhrnstromDepartment of Mathematical SciencesNorwegian University of Science and [email protected]

MS91

Traveling Surface Waves of Moderate Amplitude inShallow Water

We study traveling wave solutions of an equation for sur-face waves of moderate amplitude arising as a shallow waterapproximation of the Euler equations for inviscid, incom-pressible and homogenous fluids. We obtain solitary wavesof elevation and depression, including a family of solitarywaves with compact support, where the amplitude may in-crease or decrease with respect to the wave speed. Ourapproach is based on techniques from dynamical systemsand relies on a reformulation of the evolution equation asan autonomous Hamiltonian system which facilitates anexplicit expression for bounded orbits in the phase planeto establish existence of the corresponding periodic andsolitary traveling wave solutions.


NW14 Abstracts 133

Armengol GasullUniversitat Autnoma de BarcelonaDepartament de [email protected]

MS92

Variational Models and Energy Landscapes Asso-ciated with Self-Assembly

In this talk, I will address two paradigms for self-assembly.The first is via phase-field, energy-driven pattern formationinduced by competing short and long-range interactions.A nonlocal perturbation (of Coulombic-type) to the well-known Ginzburg-Landau/Cahn-Hilliard free energy givesrise to a mathematical paradigm with a rich and com-plex energy landscape. I will discuss some recent work(with Dave Shirokoff and J.C. Nave at McGill) on devel-oping methods for (i) assessing whether or not a particularmetastable state is a global minimizer and (ii) navigatingfrom metastable states to states of lower energy. The sec-ond paradigm is purely geometric and finite-dimensional:Centroidal Voronoi tessellations (CVT) of rigid bodies. Iwill introduce a new fast algorithm for simulations of CVTsof rigid bodies in 2D and 3D and focus on the CVT energylandscape. This is joint work with Lisa Larsson and J.C.Nave at McGill.

Rustum ChoksiDepartment of MathematicsMcGill [email protected]

MS92

A Generalized Otha-Kawasaki Model with Asym-metric Long Range Interactions

Energy-driven pattern formation induced by interactionson various scales is common in many physical systems. TheOhta-Kawasaki model is a classic nonlocal Cahn-Hilliardmodel which gives rise to pattern formation driven by thecompetition between short and long range interactions be-tween phases A and B. The interactions described in theOtha-Kawasaki model are symmetric, i.e., phase A inter-acts with phase B in the same way phase B interacts withphase A. Therefore, the only way to break symmetry is byintroducing mass asymmetry between phase A and phaseB, a parameter which is not directly related to long rangeinteractions. In this talk, I will present a Generalized Otha-Kawasaki Model with asymmetric long range interactions,whose derivation is motivated from a model of a binarymixture of charged phases. Of particular interest is themass symmetric case, as in this case, any asymmetry be-tween the two phases is directly related to the nature oflong-range interaction. I will present a systematic analy-sis of the equation. In particular, I will demonstrate thatproper tuning of the long range interaction gives rise topatterns which cannot exist in the Otha-Kawasaki model,and show that it is possible to attain isolated structures.

Nir GavishDepartment of MathematicsTechnion [email protected]

MS92

Competitive Geometric Evolution of Network Mor-

phologies

Abstract: Functionalized polymer membranes have astrong affinity for solvent, imbibing it to form charge-linednetworks which serve as charge-selective ion conductionsin a host of energy conversion applications. We present acontinuummodel, based upon a reformulation of the Cahn-Hilliard free energy, which incorporates solvation energyand counter-ion entropy to stabilize a host of network mor-phologies. We derive geometric evolution for co-dimension1 bilayers and co-dimension two pore morphologies andshow that the system possesses a simple mechanism forcompetitive evolution and bifurcation of co-existing net-works through the common far-field chemical potential.

Keith PromislowMichigan State [email protected]

Shibin DaiDepartment of MathematicsNew Mexico State [email protected]

Greg HayrapetyanDepartment of MathematicsCarnegie Mellon [email protected]

MS92

Multiple Water-Vegetation Feedback Loops Leadto Complex Vegetation Diversity Through Com-peting Turing Mechanisms

In my presentation I will use the context of dryland vege-tation to study a general problem of complex pattern form-ing systems - multiple pattern-forming instabilities that aredriven by distinct mechanisms but share the same spectralproperties. This study shows that the co-occurrence of twoTuring instabilities, when the driving mechanisms coun-teract each other in some region of the parameter space,results in the growth of a single mode rather than two inter-acting modes. The interplay between the two mechanismscompensates for the simpler dynamics of a single mode byinducing a wider variety of patterns, which implies higherbiodiversity in dryland ecosystems.

Shai Kinast, Yuval R. Zelnik, Golan BelDepartment of Solar Energy and Environmental PhysicsBen-Gurion [email protected], [email protected],[email protected]

Ehud MeronBen-Gurion [email protected]

MS93

Some Results About the Relativistic NLS Equation

We study the existence of ground states of the nonlinear pseudo-relativistic Schrodinger equation iψt =(√m2 − ∂2

x −m)ψ − |ψ|2ψ, by using a suitable adapta-

tion of the concentration-compactness principle. We proveexistence of the boosted ground states with profile ϕv ∈H1/2 (R). Also, we present results on the regularity of theground states and on the weak orbital stability of the flowof the equation. In addition we present an efficient nu-merical method to compute the profile ϕv of the boosted

134 NW14 Abstracts

ground state solution.

Juan Pablo BorgnaUniversidad Nacional General [email protected]

MS93

Interaction of Dark Nonlocal Solitons

In typical nonlinear media the response to the propagatingwave in a particular point is determined by the intensityof the wave in the same point. On the other hand, in me-dia with nonlocal nonlinearity the nonlinear response ina particular location depends on the strength of the wavein a certain neighbourhood of this location. Nonlocalityappears to be a generic feature of various nonlinear sys-tems ranging from optical beams to matter waves. It mayresult from certain transport processes such as, atom dif-fusion, heat transfer or the long range of the inter-particleinteraction as in the case of nematic liquid crystals. Such aspatially nonlocal nonlinear response is also inherent to co-herent excitations of Bose-Einstein condensates where it isdue to the finite range of the inter-particle interaction po-tential. Propagation of waves in nonlocal media has beenextensively studied both theoretically and experimentallyin last decade. It turns out that nonlocality may dramat-ically affect propagation of waves, their localization andstability. In particular, it has been shown that while nonlo-cality generally slows down modulational instability it mayactually promote it in defocusing media if the nonlocal re-sponse function is sufficiently flat. Moreover, nonlocalityhas been shown to arrest collapse of finite beams and stabi-lize spatial solitons, including vortex and rotating solitons.In addition nonlocal response of the medium drastically af-fects soliton interaction. In this talk we will discuss propa-gation of dark spatial solitons in spatially nonlocal media.I will show how nonlocality affects properties of individ-ual dark solitons and their interaction. In particular wedemonstrate that nonlocality introduces attractive forcebetween normally repelling dark solitons and ultimatelylead to the formation of their bound states. Our analyticaland numerical results are confirmed by experiments withspatial dark solitons in weakly absorbing liquids.

W. KrolikowskiAustralian National [email protected]

MS93

Optical Solitons in Nematic Liquid Crystals: Con-tinuous and Discrete Models

We present some results on optical solitons in nematic liq-uid crystals, and in waveguide arrays built from liquid crys-tals. The corresponding models are continuous and discretecubic NLS equations with Hartee-type nonlinearities thatinvolve Bessel potentials. We first review results on en-ergy minimizing solitary wave solutions for the continuous2-D case. We show the existence of smooth, radial, andmonotonic (up to symmetries) sollitons, and we also showthat these solutions can only exist above a power thresh-old. This is joint work with T. Marchant, U. Wollongong,Australia. We also report on more recent work on the dis-crete 1-D problem, where we discuss existence and stabilityof various types of breather solutions.

Panayotis PanayotarosDepto. Matematicas y MecanicaIIMAS-UNAM

[email protected]

MS94

Mixing in Stratified Shear Flows: The Central Roleof Coherent Structures

Stratified shear flow instabilities can modulate, and in somecircumstances significantly accelerate, the transition to tur-bulence in stratified fluids, which are very common in theenvironment. We demonstrate that the life-cycles of suchcoherent vortical primary and secondary instabilities playa central role in the commonly observed non-monotonicdependence of turbulent mixing on overall stratification,leading, through a classical physical mechanism first iden-tified by Phillips, to the inevitable, generic development oflayers in stratified fluids.

Colm-cille CaulfieldDAMPTCambridge [email protected]

Ali MashayekMITali [email protected]

W. Richard PeltierPhysicsUniversity of [email protected]

MS94

Large Amplitude Solitary Waves and DispersiveShock Waves in Conduits of Viscous Liquids

A dispersive shock wave (DSW) represents the combina-tion of solitary and linear dispersive wave phenomena intoone coherent structure. DSWs are therefore fundamen-tal nonlinear structures that can occur in any conservativehydrodynamic setting, e.g., superfluids and ”optical flu-ids”. Experimental studies of DSWs in all media have beenrestricted by inherent physical limitations such as multi-dimensional instabilities, difficulties in capturing dynami-cal information, and, eventually, dissipation. These limitDSW amplitudes, evolution time, and spatial extent. Inthis talk, a new medium is proposed in which to studyDSWs that overcomes all of these difficulties, allowing forthe detailed, visual investigation of dispersive hydrody-namic phenomena. The vertical evolution of the interfacebetween a buoyant, viscous liquid conduit surrounded bya miscible, much more viscous fluid exhibits nonlinear self-steepening (wave breaking), dispersion, and no measurabledissipation. First, it will be shown experimentally and the-oretically that the three Lax categories of KdV two-solitoninteraction geometries extend into the strongly nonlinearregime. Then, DSW experiments and novel DSW-solitoninteraction behaviors will be presented and compared withmodulation theory. The talk will cover multiple scales,from the microscopic (Navier-Stokes), mesoscopic (interfa-cial conduit equation), and macroscopic (Whitham modu-lation equations), to the truth (experiments).


Nicholas K. LowmanDepartment of MathematicsNorth Carolina State University

NW14 Abstracts 135

[email protected]

Gennady ElLoughborough University, United [email protected]

MS94

Buoyant Jets and Vortex Rings in Stratification

We present theoretical, computational, and experimentalstudies of the motion of buoyant fluid through a stratifiedbackground density field focusing on the evolution of jetsand vortex rings impinging upon sharp stratification. Bothcases depict an interesting critical phenomena in which thebuoyant fluid may escape or be trapped as the propagationdistance is varied. For the case of jets, an exact solutionis derived for the Morton-Taylor-Turner closure hierarchywhich yields a simple formula for this critical distance, bothwith and without a nonlinear ”entropy” condition. Theseformulae will be compared directly to experimental mea-surements. Additionally, analysis will be shown demon-strating that the sharp two-layer background is the optimalstably stratified mixer. For the case of the buoyant vortexring, full DNS simulations of the evolving ring impingingupon sharp stratification will compared directly with ex-perimental measurements of the critical length.

Richard McLaughlinUNC Chapel [email protected]

MS94

On the Extreme Runup of Long Surface Waves ona Vertical Barrier

The runup of long, strongly nonlinear waves impinging ona vertical barrier can result in a remarkable amplification(beyond 6 times) of the far-field amplitude of incomingwaves. Such an extreme runup is the result of an evolu-tion process in which long waves experience strong ampli-fication under the combined action of nonlinear steepeningand dispersion, followed by the formation of undular bores.In this work we study and discuss the conditions that re-sult optimal for producing vertical runup, as well as someof its consequences, by means of numerical simulations ofthe free-surface Euler equations. In particular, we analyzethe pressure fluctuations on the wall during strong runupcycles. We show that non-hydrostatic effects can stronglyaffect the dynamic loads exerted on the wall, and that, asa consequence, the high-frequency component of the pres-sure loads is significantly enhanced with respect to that ofthe wave spectrum itself. This observation suggests thatalso long oceanic waves can act as a source of seismic noise.

Claudio ViottiDepartment of Mathematical SciencesUniversity College [email protected]

PP1

Bifurcation of Travelling Waves in Nonlinear Mag-netic Metamaterials

We consider a model of one-dimensional metamaterialformed by a discrete array of nonlinear split-ring resonatorswhere each ring interacts with its nearest neighbors. Atfirst we study this problem without taking into accountthe normalized electro-motive force and the loss coeffi-

cient. The existence and uniqueness results of periodic andasymptotic travelling waves of the system are presented,using dynamical system methods. We compare our analyt-ical results with numerical simulation.

Makrina Agaoglou, Makrina AgaoglouAristotle University of ThessalonikiUniversity of Essexmakrina [email protected], makrina [email protected]



Giorgos P. VeldesNationaland Kapodistrian University of [email protected]

PP1

The Dual-Weighted Residual Method Applied to aDiscontinuous Galerkin Discretization for the Shal-low Water Wave Equations

The dual-weighted residual (DWR) method provides anerror estimator which can be used as a mesh refinementcriterion for adaptive methods.Our aim is to use the DWRscheme for goal oriented mesh refinement applied to a dis-continuous Galerkin (DG) discretization of the shallow wa-ter equations. Since the DG method allows discontinu-ous solutions the dual equations have discontinuous coeffi-cients. We solve the dual equations also by the DGmethod,using a Riemann solver designed to handle discontinuouscoefficients.

Susanne Beckers, Jorn BehrensKlimaCampus, University of [email protected], [email protected]

Winnifried WollnerUniveristy of [email protected]

PP1

Dipolar Bose-Einstein Condensates

In this poster we analyze the Gross-Pitaevskii equationmodeling the dynamics of dipolar Bose-Einstein conden-sates:

iψt(x, t) = −1

2Δψ(x, t) + V (x)ψ(x, t)

+α |ψ(x, t)|2 ψ(x, t) + β(W ∗ |ψ|2)ψ(x, t),t ∈ R>0, x ∈ R

3.

where V (x) = ω1x21 + ω2x

22 + ω3x

23 states for a double-well

harmonic trap potential (with ωk being the trap frecuency

in xk direction) and W (x) = 1−3(x·n)2

|x|3 is the kernel of the

dipolar interaction potential (with n ∈ R3, |n| = 1, being

the dipole axis).

We show some known facts concerning the existence

136 NW14 Abstracts

of solutions and well-posedness and present a time-splitting method for computing the dynamics.

Roberto I. BenUniversidad Nacional de General [email protected]

PP1

Oscillatory Pulses in the Fitzhugh-Nagumo Equa-tion

It is well known that the FitzHugh-Nagumo system ex-hibits stable, spatially monotone traveling pulses. Also,there is numerical evidence for the existence of spatiallyoscillatory pulses, which would allow for the constructionof multi-pulses. Here, we show the existence of oscillatorypulses rigorously, using geometric blow-up techniques andsingular perturbation theory.

Paul A. CarterDepartment of MathematicsBrown [email protected]

Bjorn SandstedeBrown Universitybjorn [email protected]

PP1

Stability of Spatially Periodic Pulse Solutions inGeneral Singularly Perturbed Reaction-DiffusionSystems

The spectral stability of spatially periodic pulse solutions isstudied in a general class of singularly perturbed reaction-diffusion systems that significantly extends the theoryfor slowly non-linear equations of Gierer-Meinhardt/Gray-Scott type. The Evans function is approximated by a prod-uct of an analytic ‘fast’ component Df and a meromorphic‘slow’ component Ds, corresponding to singular limits ofthe stability problem. Stability is determined by Df , Ds

and ‘small’ spectrum around 0. Each of these aspects areanalyzed in full asymptotic detail.

Bjorn De RijkLeiden [email protected]


Jens RademacherUniversity of [email protected]

Frits VeermanOxford [email protected]

PP1

Stochastic Mode-Reduction in Models with Con-servative Fast Sub-Systems

We will consider application of the stochastic mode re-duction to multi-scale models with deterministic energy-conserving fast sub-system. Since there is energy exchangebetween the fast conservative sub-system and the slow vari-

ables, it is necessary to explicitly keep track of the energy ofthe fast sub-system. Therefore, we develop a new stochas-tic mode reduction process in this case by introducing en-ergy of the fast subsystem as an additional hidden slowvariable. We use several prototype models to illustrate theapproach.

Ankita JainDept of Applied and Computational Mathematics andStatisticsUniversity of Notre [email protected]

PP1

Stochastic Analysis of Turbulent Mixing

We study fluid mixing layers which grow out of acceler-ation driven instabilities, including the classical cases ofRayleigh-Taylor instability, driven by a steady accelerationand Richtmyer-Meshkov instability, driven by an impulsiveacceleration. Numerical simulations of the microphysicalequations of fluid mixing are validated through compari-son to laboratory experiments. We mathematically analyzeproperties of fluid mixing and averaged equations.

Hyeonseong JinJeju National [email protected]

PP1

Abundant Soliton Solutions of the General Nonlo-cal Nonlinear Schrodinger System with the Exter-nal Field

Periodic and quasi-periodic breather multi-solitons solu-tions, dipole-type breather soliton solution, the rogue wavesolution and the fission soliton solution of the general non-local Schrodinger equation are derived by using the similar-ity transformation and manipulating the external potentialfunction. And the stability of the exact solitary wave so-lutions with the white noise perturbation is investigatednumerically..

Ji LinInstitute of Nonlinear Physics,Zhejiang normal [email protected]

Xiaoyan TangEast China Normal [email protected]

PP1

Elastic Nonlineal Model for a UnidimensionalChain with Clustering Zones

We study weakly nonlineal localized oscillations in an quar-tic elastic network model. Elastic network models describesets of particles interacting through pairwise elastic po-tentials of finite range, We use a small displacement as-sumption to derive a quartic FPU-type model in which thenumber of interacting neighbours depends on the site. Thespatial inhomogeneity of the interaction, specifically thepresence of clusters of particles that interact with manyneighbours, leads to the existence localized linear modes.Additionally we show examples where the properties of thelinear spectrum, and the nonlinear mode interaction coeffi-cients allow us to bring the system into a normal form that

NW14 Abstracts 137

has invariant subspaces with additional symmetries andperiodic orbits that represent spatially localized motions.

Francisco J. MartinezUniversidad Nacional Autonoma de [email protected]

PP1

Scattering from a Large Cylinder with a Cluster ofEccentrically Embedded Cores

The onset of Anderson localization at millimeter/sub-millimeter wavelengths is experimentally studied by exam-ining a scale model of cylindrical scatterers embedded intoa large host cylinder. Analytic methods are developed tocompare the laboratory measurements with the theoreticalpredictions. A numerical implementation of these methodsallows us to gain physical insight into the onset of Andersonlocalization in two and three dimensions.

Brittany MccollomColorado School of [email protected]

Alex YuffaU.S. Army Research Laboratory2800 Powder Mill Road, Adelphi, MD [email protected]

PP1

Oscillons Near Hopf Bifurcations of Planar Reac-tion Diffusion Equations

Oscillons are planar, spatially localized, temporally oscil-lating, radially symmetric structures. They have beenobserved in several experimental media, including fluids,granular particles, and chemical reactions. Oscillons of-ten arise near forced Hopf bifurcations. Such systems aremodeled mathematically by the forced complex Ginzburg-Landau equation (CGL). We present a proof of the exis-tence of oscillons CGL through a geometric blow-up anal-ysis. Our analysis is complemented by a numerical contin-uation study of oscillons using Matlab and AUTO.

Kelly Mcquighan, Bjorn SandstedeBrown Universitykelly [email protected],bjorn [email protected]

PP1

Stability of Morphodynamical Equilibria in TidalBasins

Interesting patterns are observed in the tidal basins inThe Wadden Sea. To get a better understanding of thesepatterns, a morphodynamical model is constructed. Thismodel describes the interaction between water motion, sed-iment transport and bed evolution. The goal is to find themorphodynamic equilibria, to investigate their sensitivityto parameter variations, and to understand the physicalmechanisms resulting in these equilibria.

Corine J. MeermanLeiden UniversityMathematical [email protected]

Vivi Rottschafer

Department of MathematicsLeiden [email protected]

Henk SchuttelaarsDelft University of TechnologyDepartment of Applied Mathematical [email protected]

PP1

Hydrodynamic Rogue Waves

The poster primarily discusses the hierarchy of rogue wavestructures generated by the Peregrine soliton in envelopeequations. This covers how to generate higher order so-lutions from those known and how these behave in higherorder models, such as the Dysthe equation. The poster alsotouches on the stability of the Peregrine soliton to differentkinds of disturbances and how these can be generalised toother rational solutions of the Nonlinear Schrodinger equa-tion.

Daniel RatliffUniversity of [email protected]

PP1

Bifurcation of Travelling Waves in Nonlinear Mag-netic Meta-Materials

We consider a model of one-dimensional meta-materialformed by a discrete array of nonlinear split-ring resonatorswhere each ring interacts with its nearest neighbors. Atfirst we study this problem without taking into accountthe normalized electro-motive force and the loss coeffi-cient. The existence and uniqueness results of periodic andasymptotic travelling waves of the system are presented,using dynamical system methods. We compare our analyt-ical results with numerical simulation.


Hadi SussantoUniveristy of [email protected]

G.P VeldesTechnological Institution of [email protected]

PP1

Tracking Pattern Evolution Beyond Center Mani-fold Reductions with Singular Perturbations

We consider 2-component, singularly perturbed PDE-systems with a known stability spectrum, close to a bi-furcation. A method which reduces them to 2D systemsof ODEs governing the flow on an exponentially attracting2D manifold, is presented. Other than center manifold re-duction, this method remains robust even if the primaryeigenvalue is of the same asymptotic magnitude as othereigenvalues. We also show explicit systems for which thereduction is 3D or 5D, and contains chaos.

Lotte SewaltLeiden University

138 NW14 Abstracts

[email protected]


Vivi RottschaferDepartment of MathematicsLeiden [email protected]

Antonios ZagarisUniversiteit [email protected]

PP1

Reflection and Transmission of Plane Quasi Longi-tudinal Waves at Semiconductor Elastic Solid In-terface

This paper deals with the study of reflection and transmis-sion characteristics of acoustic waves at the interface of asemiconductor half-space and elastic solid.

Amit SharmaNational Institute of Technology [email protected]

PP1

Robust Pulse Generators in An Excitable Mediumwith Jump-Type Heterogeneity

We study a spontaneous pulse-generating mechanism oc-curred in an excitable medium with jump type heterogene-ity. We investigate firstly the conditions for the onset ofrobust-type PGs, and secondly, we show the organizingcenter of their complex ordered sequence of pulse genera-tion manners. To explore the global bifurcation structureof heterogeneity-induced ordered patterns (HIOPs) includ-ing PGs, we devise numerical frameworks to trace the long-term behaviors of PGs as periodic solutions, and we detectthe associated terminal homoclinic orbits that are homo-clinic to a special type of HIOPs with a hyperbolic saddle.

Takashi TeramotoChitose Institute of Science and [email protected]

PP1

On the Statistics of Localized Rogue Wave Struc-tures in Spontaneous Modulation Instability

We use numerical simulations of the stochastic NLSE toinvestigate the statistics of emergent intensity peaks in thechaotic field generated from spontaneous modulation in-stability. We show that these emergent structures displaytime and space properties well-described by analytic NLSEsolutions including Akhmediev breather, Peregrine Solitonand Kuznetsov-Ma soliton forms. Examining the statisticsof these structures allows us to associate the highest in-tensity rogue wave peaks as due to higher-order breathersuperpositions.

John DudleyUniversite de Franche-Comte, Institut FEMTO-ST, UFRSciences16, route de Gray, 25030 Besancon Cedex, [email protected]

Shanti ToengerCNRS Institut FEMTO-STBesancon, [email protected]

Goery GentyTampere University of TechnologyTampere, [email protected]

Frederic DiasUniversity College DublinSchool of Mathematical [email protected]

PP1

Evolution Equations for Weakly Nonlinear InternalOcean Waves

We follow a perturbation approach to derive an evolutionequation from the equations of momentum for long, weaklynonlinear internal ocean waves for a two-layer system. Atthe second order of the momentum equations, the extendedKortewegde Vries equation was derived in the literature.For this work, we will attempt to rewrite the momentumequations at the third order and higher order.

Eric J. Tovar, Daqi XinThe University of Texas-Pan [email protected], [email protected]

Zhijun QiaoDepartment of [email protected]

PP1

Soliton Interactions in the Sasa-Satsuma Equationon Nonzero Backgrounds

In this poster, we obtain two families of anti-dark solitonsolutions of the Sasa-Satsuma equation on nonzero back-grounds, one of which can the W-shaped solitary struc-ture. The anti-dark solitons admit both the elastic colli-sions and resonant interactions, which has been first re-ported in a one-dimensional nonlinear dispersive equationwith only one field. In general, the solutions can exhibitmore complicated phenomena which are combined of elas-tic and resonant interactions.

Tao XuChina University of Petroleum, [email protected]

Min LiNorth China Electric Power [email protected]


NW14 Speaker and Organizer Index

Italicized names indicate session organizers.


Bridges, Tom J., IP8, 1:00 Thu

Bridges, Tom J., MS80, 2:00 Thu



Bronski, Jared, IP1, 10:45 Mon

Brubaker, Nicholas D., MS66, 6:00 Wed

Buckingham, Robert, MS40, 5:00 Tue

Burns, Keaton, CP9, 3:40 Wed

Bushby, Paul J., MS73, 9:10 Thu

Byrne, Greg A., MS39, 3:30 Tue

CCalini, Annalisa M., MS54, 8:10 Wed

Calini, Annalisa M., MS62, 2:00 Wed



Camassa, Roberto, MS56, 3:30 Wed

Camassa, Roberto, MS87, 2:00 Thu



Caputo, Jean-Guy, MS79, 8:10 Thu

Caputo, Jean-Guy, MS79, 8:40 Thu

Carles, Remi, MS3, 8:00 Mon




Carr, Magda, MS81, 2:00 Thu

Carretero, Ricardo, MS2, 8:00 Mon

Cartarius, Holger, MS59, 3:30 Wed

Carter, John, MS46, 5:30 Tue

Carter, Paul A., PP1, 8:00 Tue

Cascaval, Radu C., MS42, 5:30 Tue

Caulfield, Colm-cille, MS94, 5:30 Thu

Chakravarty, Sarbarish, MS76, 9:40 Thu

Chardard, Frederic, MS80, 2:00 Thu



Chaudhary, Osman, MS8, 9:00 Mon

Chembo, Yanne, MS20, 5:00 Mon

Chen, Chiao-Nen, MS80, 2:30 Thu

Chen, Yong, MS76, 9:10 Thu

Cheng, Bin, CP9, 2:00 Wed

Chertock, Alina, MS61, 2:00 Wed


AAbdullaev, Fatkhulla, MS59, 2:30 Wed

Ablowitz, Mark, SP1, 8:15 Mon

Aceves, Alejandro, MS27, 9:10 Tue

Aceves, Alejandro, MS56, 2:30 Wed

Aceves, Alejandro, MS79, 8:10 Thu

Adami, Riccardo, MS3, 9:00 Mon

Adami, Riccardo, MS42, 5:00 Tue

Aftalion, Amandine, MS37, 2:30 Tue

Agaoglou, Makrina, PP1, 8:00 Tue

Akkoyunlu, Canan, CP2, 3:00 Mon

Alejo, Miguel, MS15, 2:00 Mon

Alemi Ardakani, Hamid, MS80, 3:30 Thu

Alexander, Tristram J., CP8, 9:10 Wed

Allard, Jun, MS6, 8:30 Mon

Al-Nahdi, Abeer, CP7, 6:10 Tue

Ambrose, David, MS58, 3:00 Wed

Anco, Stephen, MS15, 2:00 Mon



Anco, Stephen, MS62, 2:30 Wed

Ania Castañón, Juan Diego, MS75, 8:10 Thu

Ashton, Anthony, MS17, 4:30 Mon

Athanassoulis, Agisilaos, MS11, 2:00 Mon

Avitabile, Daniele, MS73, 8:10 Thu

BBachman, Scott, MS18, 5:00 Mon

Baggaley, Andrew, MS31, 9:40 Tue

Baker, Ruth E., MS6, 8:00 Mon

Barashenkov, Igor, MS43, 5:30 Tue

Barenghi, Carlo F., MS2, 8:30 Mon

Barenghi, Carlo F., MS31, 8:10 Tue

Barkley, Dwight, CP5, 8:10 Tue

Beaume, Cedric, MS65, 4:30 Wed

Beaume, Cedric, MS73, 8:10 Thu

Beaume, Cedric, MS73, 8:40 Thu

Beck, Margaret, MS8, 8:00 Mon

Becker, Christoph, MS2, 9:00 Mon

Beckers, Susanne, PP1, 8:00 Tue

Bedrossian, Jacob, MS8, 8:00 Mon

Bedrossian, Jacob, MS16, 3:00 Mon

Beljadid, Abdelaziz, MS69, 5:30 Wed

Bellsky, Thomas, MS82, 2:00 Thu



Belmonte-Beitia, Juan, CP5, 9:50 Tue

Ben, Roberto I., PP1, 8:00 Tue

Bender, Carl M., MS43, 4:30 Tue

Berloff, Natalia G., MS2, 8:00 Mon

Berwald, Jesse, MS90, 6:00 Thu

Beyn, Wolf-Juergen, MS21, 5:30 Mon

Bidegaray-Fesquet, Brigitte, MS4, 9:00 Mon

Biktashev, Vadim N., MS47, 5:30 Tue

Biktasheva, Irina, MS39, 2:00 Tue

Biktasheva, Irina, MS39, 2:00 Tue

Biondini, Gino, MS25, 8:10 Tue



Biondini, Gino, MS70, 5:00 Wed

Bizon, Piotr, MS37, 3:00 Tue

Blanchet, Adrien, MS37, 3:30 Tue

Blyth, Mark, MS89, 6:00 Thu

Boechler, Nicholas, MS12, 3:00 Mon

Bokhove, Onno, MS18, 4:30 Mon

Bona, Jerry, MS17, 5:00 Mon

Bookman, Lake, CP3, 4:50 Mon

Borgna, Juan Pablo, MS93, 5:00 Thu

Borluk, Handan, MS91, 4:30 Thu

Borluk, Handan, MS91, 6:00 Thu

Boscolo, Sonia, MS67, 4:30 Wed

Boscolo, Sonia, MS67, 4:30 Wed

Boscolo, Sonia, MS75, 8:10 Thu

Boscolo, Sonia, MS83, 2:00 Thu

Bouchet, Freddy, MS8, 8:30 Mon

Boutet de Monvel, Anne, MS25, 9:10 Tue

Boyd, John P., CP3, 4:30 Mon

Bressloff, Paul C., IP5, 10:45 Wed

Bressloff, Paul C., MS6, 8:00 Mon

Bressloff, Paul C., MS6, 9:30 Mon




Chiba, Hayato, MS24, 5:00 Mon

Chien, Cheng-Sheng, CP12, 2:00 Thu

Chirilus-Bruckner, Martina, MS34, 2:00 Tue

Chirilus-Bruckner, Martina, MS49, 9:10 Wed

Choi, Wooyoung, MS89, 4:30 Thu

Choi, Yung-Sze, MS88, 5:30 Thu

Choksi, Rustum, MS92, 5:00 Thu

Chomaz, Jean-Marc, MS10, 2:30 Mon

Chong, Christopher, MS4, 8:00 Mon



Christodoulides, Demetrios, MS43, 6:00 Tue

Christodoulides, Paul, CP11, 9:50 Thu

Chumakova, Lyubov, MS26, 9:40 Tue

Churkin, Dmitry, MS27, 9:40 Tue

Cisneros, Luis, MS77, 9:40 Thu

Coillet, Aurelien, MS28, 9:10 Tue

Cole, Justin, CP4, 8:10 Tue

Colinet, Pierre, MS86, 3:00 Thu

Comech, Andrew, MS36, 3:30 Tue

Conti, Claudio, MS75, 9:10 Thu

Cox, Graham, MS13, 3:30 Mon

Cox, Graham, MS82, 2:00 Thu

Cox, Graham, MS90, 4:30 Thu

Crowdy, Darren G., MS9, 3:00 Mon

Cucinotta, Annamaria, MS83, 3:30 Thu

DDaraio, Chiara, IP6, 1:00 Wed

Dawes, Jonathan, MS30, 8:10 Tue

De Angelis, Costantino, MS83, 2:00 Thu

De Leo, Mariano, MS85, 2:30 Thu

De Rijk, Björn, PP1, 8:00 Tue

Deconinck, Bernard, MS1, 8:00 Mon



Deconinck, Bernard, MS50, 8:10 Wed



Demontis, Francesco, MS54, 8:10 Wed



Deng, Wen, MS8, 9:30 Mon

Derevyanko, Stanislav, CP12, 2:40 Thu

Derks, Gianne, MS21, 4:30 Mon

Dias, Juliana F., MS41, 4:30 Tue

Dierckx, Hans, MS47, 6:00 Tue

Dirr, Nicolas, MS5, 9:00 Mon

Doelman, Arjen, MS49, 8:10 Wed

Dohnal, Tomas, MS27, 8:10 Tue




Doliwa, Adam, MS54, 9:10 Wed

Dudley, John, MS67, 6:00 Wed

Duruk Mutlubas, Nilay, CP11, 8:10 Thu

Duruk Mutlubas, Nilay, MS91, 4:30 Thu

Duruk Mutlubas, Nilay, MS91, 5:30 Thu

EEhrnstrom, Mats, MS38, 2:00 Tue

Ehrnstrom, Mats, MS46, 4:30 Tue

Ehrnstrom, Mats, MS91, 4:30 Thu

El, Gennady, MS87, 3:30 Thu

Entcheva, Emilia, MS39, 2:30 Tue

Erbay, Husnu Ata, MS46, 5:00 Tue

Esler, Gavin, MS18, 6:00 Mon

FFagerstrom, Emily, MS40, 5:30 Tue

Faria, Luiz, CP10, 5:30 Wed

Faye, Gregory, MS16, 2:00 Mon

Faye, Gregory, MS24, 4:30 Mon

Feng, Bao-Feng, MS52, 8:10 Wed




Feng, Bao-Feng, MS76, 8:10 Thu

Finot, Christophe, MS67, 5:00 Wed

Fokas, Athanassios S., MS1, 8:30 Mon

Fokas, Athanassios S., MS25, 8:10 Tue

Fokas, Thanasis, IP2, 1:00 Mon

Frantzeskakis, D.J., MS63, 2:30 Wed

GGabitov, Ildar R., MS48, 8:40 Wed

Gallardo, Jose M., MS69, 4:30 Wed

Garcia-Morales, Vladimir, MS84, 3:00 Thu

Gat, Omri, MS20, 4:30 Mon

Gat, Omri, MS28, 8:10 Tue



Gavish, Nir, MS84, 2:00 Thu



Gavrilyuk, Sergey, MS88, 5:00 Thu

Gelens, Lendert, MS65, 5:00 Wed

Gemmer, John A., MS74, 8:40 Thu

Geyer, Anna, CP3, 5:10 Mon

Geyer, Anna, MS91, 5:00 Thu

Ghazaryan, Anna, MS13, 2:00 Mon

Ghazaryan, Anna, MS21, 4:30 Mon

Ghazaryan, Anna, MS29, 8:10 Tue



Ghazaryan, Anna, MS49, 9:40 Wed

Ghulinyan, Mher, MS35, 3:30 Tue

Giannoulis, Ioannis, MS71, 4:30 Wed

Gilson, Claire, MS52, 9:10 Wed

Goh, Ryan, CP7, 4:30 Tue

Goldobin, Denis S., MS78, 9:40 Thu

Goldstein, Ray E., MS22, 6:00 Mon

Gonzalez de Alaiza, Pedro, MS48, 9:40 Wed

Goodman, Roy, MS27, 8:40 Tue

Gordillo, Leonardo, CP3, 5:30 Mon

Gorodetsky, Michael, MS20, 4:30 Mon

Grigoriev, Roman, MS47, 4:30 Tue

Grigoriev, Roman, MS47, 4:30 Tue

Grimshaw, Roger, MS33, 3:00 Tue

Groves, Mark D., MS50, 9:40 Wed

Guenther, Uwe, MS43, 5:00 Tue



Gupta, Neelam, CP10, 4:50 Wed

Gurevich, Pavel, MS16, 3:30 Mon

Gustafson, Stephen, MS45, 4:30 Tue

Guyenne, Philippe, MS77, 8:40 Thu



HHainzl, Christian, MS45, 5:00 Tue

Hamid, Oualli, CP6, 2:40 Tue

Hansson, Tobias, MS28, 8:40 Tue

Haragus, Mariana, MS29, 8:10 Tue

Hari, Lysianne, MS11, 2:30 Mon

Hattam, Laura, CP8, 9:30 Wed

He, Jingsong, CP1, 9:40 Mon

He, Yi, MS60, 3:30 Wed

Hernandez-Duenas, Gerardo, MS10, 3:30 Mon

Herrmann, Michael, MS71, 4:30 Wed

Himonas, Alex, MS1, 9:00 Mon

Himonas, Alex, MS23, 4:30 Mon

Hitzazis, Iasonas, CP2, 2:00 Mon

Hoefer, Mark A., CP6, 2:00 Tue

Hoefer, Mark A., MS94, 6:00 Thu

Holm, Darryl D., IP7, 10:45 Thu

Holmer, Justin, MS34, 3:30 Tue

Holmes, William R., MS6, 9:00 Mon

Howard, Peter, MS21, 5:00 Mon

Hu, Xing-Biao, MS52, 8:10 Wed




Hu, Xing-Biao, MS76, 8:10 Thu

Humpherys, Jeffrey, MS44, 4:30 Tue

Hundertmark, Dirk, MS34, 3:00 Tue

Hupkes, Hermen Jan, MS16, 2:00 Mon

IIima, Makoto, CP5, 8:30 Tue

Iversen, Morten, MS87, 2:30 Thu

Ivey, Thomas, MS62, 3:00 Wed

JJacobs, Henry O., MS7, 8:00 Mon

Jacobs, Henry, MS7, 9:30 Mon

Jain, Ankita, PP1, 8:00 Tue

James, Guillaume, MS71, 4:30 Wed

Jaramillo, Gabriela, MS24, 5:30 Mon

Jin, Hyeonseong, PP1, 8:00 Tue

Jo, Tae-Chang, CP1, 8:40 Mon

Johnson, Mat, MS29, 9:40 Tue

Johnson, Mat, MS38, 3:00 Tue

Johnson, Ted, MS33, 2:00 Tue

KKaikina, Elena, MS46, 4:30 Tue

Kalisch, Henrik, MS38, 2:00 Tue

Kalisch, Henrik, MS46, 4:30 Tue

Kalisch, Henrik, MS89, 5:00 Thu

Kalliadasis, Serafim, MS78, 9:10 Thu

Kapitula, Todd, MS13, 3:00 Mon

Karper, Trygve K., MS24, 4:30 Mon

Karuppaiya, Sakkaravarthi, CP12, 3:20 Thu

Kasimov, Aslan R., CP10, 5:50 Wed

Kerswell, Rich, IP4, 1:00 Tue

Ketcheson, David I., CP11, 8:30 Thu

Kevrekidis, Panayotis, MS2, 8:00 Mon

Kevrekidis, Panayotis, MS57, 2:00 Wed

Khatri, Shilpa, MS87, 2:00 Thu



Kirr, Eduard, MS11, 3:30 Mon

Kjerland, Marc, MS82, 3:30 Thu

Klaus, Martin, MS40, 4:30 Tue

Klein, Christian, MS32, 2:30 Tue

Kochurin, Evgeny, CP11, 9:10 Thu

Koepf, Michael H., MS84, 2:30 Thu

Kollar, Richard, CP8, 8:50 Wed

Kolokolnikov, Theodore, MS24, 6:00 Mon

Konotop, Vladimir V., MS43, 4:30 Tue

Konotop, Vladimir V., MS51, 8:10 Wed




Koos, Christian, MS35, 2:30 Tue

Korotkevich, Alexander O., MS48, 8:10 Wed




Korotkevich, Alexander O., MS72, 8:10 Thu

Kottos, Tsampikos, MS51, 9:10 Wed

Kourakis, Ioannis, MS63, 3:00 Wed

Kovanis, Vassilios, MS28, 8:10 Tue

Kozlov, Nikolay, MS86, 2:30 Thu

Kralj, Samo, MS30, 9:10 Tue

Krechetnikov, Rouslan, MS14, 2:00 Mon

Krolikowski, W., MS93, 4:30 Thu

Kuehn, Christian, MS5, 8:00 Mon

Kuehn, Christian, CP8, 8:30 Wed

Kuehn, Christian, MS82, 3:00 Thu

Kurganov, Alexander, MS61, 2:00 Wed



Kurnia, Ruddy, CP11, 8:50 Thu

Kutz, J. Nathan, MS83, 3:00 Thu

LLafortune, Stephane, MS29, 9:10 Tue

Lafortune, Stephane, MS49, 8:10 Wed

Lafortune, Stephane, MS57, 2:00 Wed

Langham, Jacob, MS47, 5:00 Tue

Latushkin, Yuri, MS13, 2:00 Mon



Latushkin, Yuri, MS29, 8:10 Tue



Law, Kody, MS90, 5:30 Thu



Moore, Richard O., MS93, 4:30 Thu

Mostafazadeh, Ali, MS59, 3:00 Wed

Mouradian, Levon, MS67, 5:30 Wed

Munoz, Claudio, MS3, 9:30 Mon

Munoz, Claudio, MS15, 2:30 Mon

Muraki, David, MS18, 5:30 Mon

Murashige, Sunao, MS89, 5:30 Thu

NNachbin, Andre, MS26, 8:10 Tue

Nachbin, Andre, MS26, 8:10 Tue



Nagai, Hidetomo, MS60, 3:00 Wed

Nazari, Farshid, CP9, 3:00 Wed

Nepomnyashchy, Alexander, MS78, 8:10 Thu



Newell, Alan, MS64, 4:30 Wed

Nimmo, Jonathan, MS52, 8:10 Wed




Nimmo, Jonathan, MS76, 8:10 Thu

Novikov, Vladimir, MS23, 5:00 Mon

OOdagaki, Takashi, CP13, 5:50 Thu

Oh, Tadahiro, MS19, 5:00 Mon

Ohta, Yasuhiro, MS68, 5:00 Wed

Oliveras, Katie, MS58, 3:30 Wed

Olver, Sheehan, MS32, 3:00 Tue

Orlandi, Giandomenico, MS53, 8:10 Wed

Oron, Alex, MS86, 3:30 Thu

Ortenzi, Giovanni, MS54, 8:10 Wed



Oza, Anand, MS41, 6:00 Tue

Ozawa, Tomoki, MS2, 9:30 Mon

Manukian, Vahagn, MS57, 2:00 Wed


Marangell, Robert, MS21, 6:00 Mon

Mari Beffa, Gloria, MS54, 8:10 Wed

Martinez, Alejandro J., MS79, 9:10 Thu

Martinez, Francisco J., PP1, 8:00 Tue

Maruno, Kenichi, MS52, 8:10 Wed




Maruno, Kenichi, MS76, 8:10 Thu

Matar, Omar K., MS86, 2:00 Thu

Matsukidaira, Junta, MS60, 2:30 Wed

McCalla, Scott, MS22, 4:30 Mon

McCalla, Scott, MS66, 5:30 Wed

Mccollom, Brittany, PP1, 8:00 Tue

Mchugh, John P., CP1, 8:00 Mon

McLaughlin, Richard, MS87, 2:00 Thu



Mcquighan, Kelly, PP1, 8:00 Tue

Medvedev, Georgi S., MS16, 2:30 Mon

Meerman, Corine J., PP1, 8:00 Tue

Menyuk, Curtis R., MS20, 4:30 Mon

Menyuk, Curtis R., MS28, 8:10 Tue

Menyuk, Curtis R., MS35, 2:00 Tue

Menyuk, Curtis R., MS72, 8:10 Thu

Michor, Johanna, MS25, 9:40 Tue

Milewski, Paul A., MS26, 8:10 Tue



Milewski, Paul A., MS50, 8:10 Wed

Miller, Peter D., MS32, 2:00 Tue

Miroshnikov, Victor A., CP7, 4:50 Tue

Moldabayev, Daulet, MS46, 6:00 Tue

Moleron, Miguel, MS4, 8:00 Mon



Molina, Mario, MS63, 2:00 Wed




Lazarides, Nikos, MS55, 8:40 Wed

Lee, Long, CP3, 5:50 Mon

LeMesurier, Brenton J., MS79, 8:10 Thu

LeMesurier, Brenton J., MS79, 9:40 Thu

Lenells, Jonatan, MS9, 3:30 Mon

Li, Feng, MS20, 6:00 Mon

Li, Hongyan, CP8, 8:10 Wed

Li, Luen-Chau, MS62, 2:00 Wed

Liao, Shijun, CP6, 3:20 Tue

Lin, Ji, PP1, 8:00 Tue

Linares, Felipe, MS38, 2:00 Tue

Lindsay, Alan E., MS66, 4:30 Wed

Lindsay, Alan E., MS66, 4:30 Wed

Lindsay, Alan E., MS74, 8:10 Thu

Liu, Qingping, MS52, 9:40 Wed

Liu, Xin, MS61, 2:30 Wed

Lloyd, David, MS65, 5:30 Wed

Lo Jacono, David, MS73, 9:40 Thu

Löber, Jakob, CP6, 3:40 Tue

Lombardo, Sara, MS70, 6:00 Wed

Lord, Gabriel J., MS5, 8:30 Mon

Lou, Senyue, MS76, 8:10 Thu

Lowman, Nicholas K., CP6, 2:20 Tue

Lushnikov, Pavel M., MS48, 8:10 Wed



Lushnikov, Pavel M., MS72, 8:10 Thu

Lushnikov, Pavel M., MS72, 9:40 Thu

Luzzatto-Fegiz, Paolo, CP1, 8:20 Mon

Lyng, Gregory, MS44, 5:00 Tue

MMacNeil, Michael, MS85, 2:00 Thu

Madzvamuse, Anotida, MS14, 2:30 Mon

Maestrini, Davide, CP12, 2:20 Thu

Majumdar, Apala, MS30, 8:10 Tue

Makris, Konstantinos, MS43, 6:30 Tue

Malham, Simon, MS13, 2:30 Mon

Mancas, Stefan C., CP13, 6:10 Thu

Manton, Nicholas, MS53, 9:10 Wed

Mantzavinos, Dionyssis, MS1, 9:30 Mon




Sciberras, Luke, MS77, 9:10 Thu

Sengupta, Anupam, MS30, 9:40 Tue

Sewalt, Lotte, PP1, 8:00 Tue

Sharma, Amit, PP1, 8:00 Tue

Sharma, Vishnu D., CP6, 3:00 Tue

Sheils, Natalie E., MS1, 8:00 Mon




Sherwin, Lucy, MS31, 10:10 Tue

Shipman, Patrick, MS74, 9:10 Thu

Shklyaev, Sergey, MS78, 8:10 Thu

Shklyaev, Sergey, MS86, 2:00 Thu

Short, Martin, MS22, 4:30 Mon

Short, Martin, MS22, 4:30 Mon

Siegel, Michael, MS81, 3:00 Thu

Siero, Eric, MS82, 2:30 Thu

Sigal, Israel Michael, MS37, 2:00 Tue



Sigal, Israel Michael, MS53, 8:10 Wed

Sigal, Israel Michael, MS56, 2:00 Wed

Sivan, Yonatan, CP13, 4:50 Thu

Smith, David, MS9, 2:00 Mon

Smith, Leslie, IP3, 10:45 Tue

Smith, Leslie, MS10, 2:00 Mon

Smith, Leslie, MS18, 4:30 Mon

Sobirov, Zarif A., MS42, 6:00 Tue

Soffer, Avy, MS37, 2:00 Tue

Soffer, Avy, MS45, 4:30 Tue

Soffer, Avy, MS53, 8:10 Wed

Soffer, Avy, MS53, 9:40 Wed

Sørensen, Mads, MS79, 8:10 Thu

Sparber, Christof, MS3, 8:00 Mon




Stanislavova, Milena, MS36, 3:00 Tue

Stannat, Wilhelm, MS5, 9:30 Mon

Starosvetsky, Yuli, MS4, 9:30 Mon

Subbotin, Stanislav, CP7, 5:50 Tue

QQu, Changzheng, MS62, 3:30 Wed

Quail, Thomas D., MS39, 3:00 Tue

RRademacher, Jens, MS14, 2:00 Mon

Rademacher, Jens, MS49, 8:40 Wed

Rashkov, Peter, CP5, 9:10 Tue

Ratliff, Daniel, PP1, 8:00 Tue

Raupp, Carlos, MS41, 5:30 Tue

Reichel, Wolfgang, MS34, 2:30 Tue

Renninger, William, MS35, 3:00 Tue

Ricchiuto, Mario, MS69, 5:00 Wed

Roberts, Andrew, MS90, 5:00 Thu

Rodrigues, Miguel, MS80, 3:00 Thu

Rongy, Laurence, MS14, 3:30 Mon

Rosakis, Phoebus, MS71, 5:30 Wed

Rosales, Rodolfo R., MS26, 9:10 Tue

Rosenau, Philip, MS72, 9:10 Thu

Rothos, Vassilis M., PP1, 8:00 Tue

Rothos, Vassilis M., MS55, 8:10 Wed

Rothos, Vassilis M., MS63, 2:00 Wed

Rothos, Vassilis M., MS77, 8:10 Thu

Rottmann-Matthes, Jens, MS36, 2:00 Tue

Roudenko, Svetlana, MS19, 6:00 Mon

Roudenko, Svetlana, MS72, 8:40 Thu

Rozanova, Olga S., CP9, 3:20 Wed

Rucklidge, Alastair M., CP7, 5:30 Tue

SSalewski, Matthew, MS65, 6:00 Wed

Salman, Hayder, MS31, 8:10 Tue

Salman, Hayder, MS31, 8:40 Tue

Sandstede, Bjorn, MS5, 8:00 Mon

Sandstede, Bjorn, MS65, 4:30 Wed

Saradzhev, Fuad, CP13, 5:10 Thu

Schecter, Stephen, MS36, 2:30 Tue

Scheel, Arnd, MS16, 2:00 Mon

Scheel, Arnd, MS24, 4:30 Mon

Schubert, Roman, MS11, 3:00 Mon

Schwetlick, Hartmut, MS71, 6:00 Wed

PPage, Charlotte, MS81, 3:30 Thu

Panayotaros, Panayotis, MS77, 8:10 Thu




Parau, Emilian I., MS50, 9:10 Wed

Parau, Emilian I., MS81, 2:00 Thu

Parau, Emilian I., MS89, 4:30 Thu

Pavliotis, Greg, MS5, 8:00 Mon

Pavlov, Dmitry, MS7, 9:00 Mon

Pei, Long, MS38, 3:30 Tue

Pelinovsky, Dmitry, MS15, 2:00 Mon

Pelinovsky, Dmitry, MS23, 4:30 Mon

Pelinovsky, Dmitry, MS29, 8:40 Tue

Pelinovsky, Dmitry, MS51, 8:40 Wed

Pelloni, Beatrice, MS17, 5:30 Mon

Pennybacker, Matthew, MS66, 4:30 Wed

Pennybacker, Matthew, MS74, 8:10 Thu

Pennybacker, Matthew, MS74, 8:10 Thu

Phibanchon, Sarun, CP4, 8:50 Tue

Picozzi, Antonio, MS75, 9:40 Thu

Piltz, Sofia, CP5, 8:50 Tue

Plouraboue, Franck, MS84, 3:30 Thu

Pocovnicu, Oana, MS19, 5:30 Mon

Polezhaev, Denis A., CP7, 5:10 Tue

Porter, Mason A., MS12, 2:00 Mon

Prinari, Barbara, MS25, 8:10 Tue



Prinari, Barbara, MS70, 5:30 Wed

Promislow, Keith, MS57, 3:00 Wed

Promislow, Keith, MS92, 5:30 Thu

Putkaradze, Vakhtang, MS7, 8:00 Mon



Sukys, Jonas, MS61, 3:30 Wed

Sun, Shu-Ming, MS44, 6:00 Tue

Susanto, Hadi, MS55, 8:10 Wed



TTabak, Esteban G., MS26, 8:40 Tue

Takahashi, Daisuke, MS60, 2:00 Wed

Talukder, Muhammad, MS20, 5:30 Mon

Tang, Bao Q., CP5, 9:30 Tue

Tang, Xiaoyan, CP2, 2:20 Mon

Teramoto, Takashi, PP1, 8:00 Tue

Teschl, Gerald, MS25, 8:40 Tue

Tiglay, Feride, MS23, 5:30 Mon

Toenger, Shanti, PP1, 8:00 Tue

Topkarci, Goksu, CP11, 9:30 Thu

Tovar, Eric J., PP1, 8:00 Tue

Travers, John, MS83, 2:30 Thu

Trichtchenko, Olga, MS50, 8:10 Wed



Trogdon, Thomas, MS32, 3:30 Tue

Tsai, Je-Chiang, MS44, 5:30 Tue

Tsang, Yue-Kin, CP9, 2:20 Wed

Tseluiko, Dmitri, CP12, 3:40 Thu

Tsironis, George, MS55, 9:10 Wed

Tsitsas, Nikolaos L., MS55, 8:10 Wed

Turitsyn, Sergei, MS48, 9:10 Wed

Turitsyn, Sergei, MS67, 4:30 Wed

Turitsyn, Sergei, MS75, 8:10 Thu

Turitsyn, Sergei, MS83, 2:00 Thu

Turner, Matthew R., CP10, 5:10 Wed

Tzou, Justin C., MS66, 5:00 Wed

UUecker, Hannes, MS27, 8:10 Tue

Uecker, Hannes, MS34, 2:00 Tue



Uminsky, David T., MS7, 8:30 Mon

VVakakis, Alexander, MS4, 8:30 Mon

Valchev, Tihomir I., CP4, 9:10 Tue

van den Bremer, Ton, MS81, 2:30 Thu

Van der Mee, Cornelis, MS70, 4:30 Wed

Vanden-Broeck, Jean-Marc, MS33, 2:30 Tue

Vanden-Broeck, Jean-Marc, MS58, 2:00 Wed

Vanneste, Jacques, MS10, 2:00 Mon

Varatharajah, Rajah P., CP13, 4:30 Thu

Vasan, Vishal, MS9, 2:30 Mon

Vasil, Geoffrey M., CP9, 2:40 Wed

Veerman, Frits, MS14, 2:00 Mon

Vega, Jose Manuel, MS78, 8:10 Thu

Venkataraman, Chandrashekar, MS14, 3:00 Mon

Viotti, Claudio, MS94, 5:00 Thu

Visciglia, Nicola, MS3, 8:30 Mon

Vitale, Federica, MS40, 6:00 Tue

Vitelli, Vincenzo, MS30, 8:40 Tue

Volkening, Alexandria, MS22, 5:00 Mon

von Brecht, James, MS22, 5:30 Mon

WWabnitz, Stefan, MS20, 4:30 Mon

Wabnitz, Stefan, MS28, 8:10 Tue

Wabnitz, Stefan, MS35, 2:00 Tue

Wabnitz, Stefan, MS75, 8:40 Thu

Wahlen, Erik, MS38, 2:30 Tue

Walmsley, Paul, MS31, 9:10 Tue

Wang, Danhua, CP12, 3:00 Thu

Wang, Jin-Ping, MS54, 8:40 Wed

Wang, Qiao, MS15, 3:30 Mon

Wang, Shaokang, MS35, 2:00 Tue

Wang, Zhan, MS58, 2:30 Wed

Wattis, Jonathan, MS71, 5:00 Wed

Wayne, C. Eugene, MS8, 8:00 Mon

Wetzel, Alfredo N., CP2, 2:40 Mon

Widiasih, Esther, MS90, 4:30 Thu

Wingate, Beth, MS41, 5:00 Tue

Wu, Yuhu, CP13, 5:30 Thu

Wulff, Claudia, MS88, 4:30 Thu

Wunsch, Scott E., CP1, 9:00 Mon

XXing, Yulong, MS61, 3:00 Wed

Xu, Tao, PP1, 8:00 Tue

YYamane, Hideshi, CP4, 8:30 Tue

Yamazaki, Yohei, MS15, 3:00 Mon

Yang, Jianke, MS43, 4:30 Tue

Yang, Jianke, MS51, 8:10 Wed



Yang, Jinkyu, MS12, 2:30 Mon

Yao, Ruoxia, MS68, 6:00 Wed

Yochelis, Arik, MS84, 2:00 Thu



Yu, Jie, CP10, 4:30 Wed

ZZakharov, Vladimir E., MS48, 8:10 Wed

Zarmi, Yair, CP3, 6:10 Mon

Zeitlin, Vladimir, MS10, 3:00 Mon

Zelnik, Yuval R., MS92, 6:00 Thu

Zhang, Xizheng, CP1, 9:20 Mon

Zhang, Youjin, MS52, 8:40 Wed

Zharnitsky, Vadim, MS64, 5:30 Wed

Zhu, Zuonong, MS76, 8:40 Thu

Zimmer, Johannes, MS53, 8:40 Wed

Zykov, Vladimir, MS47, 6:30 Tue


Notes


NW14 BudgetConference BudgetSIAM Conference on Nonlinear Waves and Coherent Structures (NW14)August 11-14, 2014Churchill College, Cambridge, UK

Expected Paid Attendance 350

RevenueRegistration Income $121,240Grant to Surrey University from ONRG $7,000

Total $128,240

ExpensesPrinting $2,970Organizing Committee $2,880Invited Speakers $7,900Food and Beverage $2,178AV Equipment and Telecommunication $14,744Advertising $5,000Professional Services $64,114Conference Labor (including benefits) $24,027Other (supplies, staff travel, freight, misc.) $3,036Administrative $11,749Accounting/Distribution & Shipping $5,768Information Systems $10,316Customer Service $3,821Marketing $5,933Office Space (Building) $3,239Other SIAM Services $3,672

Total $171,347

Net Conference Expense -$43,107

Support Provided by SIAM $43,107$0

Estimated Support for Travel Awards not included above:

Early Career / Students 30 $24,450

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