Localized chaotic patterns in weakly dissipative magnetic systems

D. Laroze1,2

1Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile. 2SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom.

Localized structures can be found in many

different driven systems, like chiral bubbles in liquid crystals, current filaments in gas discharge, spots in chemical reactions, localized states in fluid surface waves, oscillons in granular media, isolated states in thermal convection, solitary waves in nonlinear optics, solitons in Bose-Einstein condensates, localized states in generic subcritical instabilities, to mention a few. Recent reviews of the state of the art can be found in Refs. [1–2]. In the case of magnetism different localized structures have been recently found, such as localized waves or two-soliton states [3–4].

Close to the parametric resonance, a generalized parametrically driven damped nonlinear Schrödinger equation is used to describe, the dynamics of weakly dissipative systems. Here the complex spatio-temporal field that satisfies this equation is denoted by Ψ. In particular, an easy-plane ferromagnetic layer in the presence of both a homogenous and a harmonic time-dependent magnetic field can be reduced to this type of equation [5].

The combined effects of parametric forcing,

spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found [6]. We discuss the parameter range where these localized structures exist. Figure 1 shows a three dimensional time-space diagram of the amplitude of Ψ in a localized chaotic regime.

Fig.1: Three-dimensional space-time diagram of the amplitude of the field Ψ. References [1] O. Descalzi, M. Clerc, S. Residori, and G. Assanto

(Eds.), Localized States in Physics: Solitons and Patterns (Springer, Berlin 2010).

[2] A. Ankiewics, N. Akhmediev, Dissipative Solitons: From Optics to Biology and Medicine (Springer, Berlin, 2008).

[3] M. G. Clerc, S. Coulibaly, and D. Laroze, PRE 77, 056209 (2008); Physica D 239, 72 (2010); EPL 97, 30006 (2012).

[4] D. Urzagasti, D. Laroze, M. G. Clerc, S. Coulibaly, and H. Pleiner, J. Appl. Phys. 111, 07D111 (2012).

[5] M. G. Clerc, S. Coulibaly, and D. Laroze, EPL 90, 38005 (2010).

[6] D. Urzagasti, D. Laroze, H. Pleiner, EPJ S.T. 223, 141 (2014).