noncommutative vortices and beach waves
DESCRIPTION
Frontiers in Nonlinear Waves in honor of Vladimir Zakharov's 70th birthday. Noncommutative vortices and beach waves. G. Cruz L.R. Juárez A. A. Minzoni M. Rosenbaum. IIMAS-FENOMEC, UNAM. Pelinovsky, Kevrekidis, Frantzeskikis 2005. Circular vortex. Peierls-Nabarro potential. Static vortex. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/1.jpg)
Noncommutative vortices and beach waves
G. Cruz
L.R. Juárez
A. A. Minzoni
M. Rosenbaum
IIMAS-FENOMEC, UNAM
Frontiers in Nonlinear Wavesin honor of Vladimir Zakharov's 70th birthday
![Page 2: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/2.jpg)
Pelinovsky, Kevrekidis, Frantzeskikis 2005
![Page 3: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/3.jpg)
Circular vortex
![Page 4: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/4.jpg)
![Page 5: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/5.jpg)
Peierls-Nabarro potential
![Page 6: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/6.jpg)
Static vortex
![Page 7: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/7.jpg)
Peierls-Nabarro potential
![Page 8: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/8.jpg)
Noncommutative NLS equation
![Page 9: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/9.jpg)
Strominger 2000.
![Page 10: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/10.jpg)
![Page 11: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/11.jpg)
Lindstrom-Rocek 2003
![Page 12: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/12.jpg)
![Page 13: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/13.jpg)
Modulation equations
The last expression is the equation of motion for the peak of the vortex, analogous to a particle in a Peierls-Nabarro potential.
![Page 14: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/14.jpg)
Large vortex with low energy
The vortex moves in the lattice generated by the *-product.
The fixed points are the equilibrium positions
![Page 15: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/15.jpg)
![Page 16: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/16.jpg)
![Page 17: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/17.jpg)
![Page 18: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/18.jpg)
![Page 19: Noncommutative vortices and beach waves](https://reader035.vdocument.in/reader035/viewer/2022062422/56812d87550346895d92988f/html5/thumbnails/19.jpg)