Nonlinear Dynamics of Layered Structures and the Generalized Sine-Lattice Equations

Abstract

We analyze nonlinear waves in layered (anisotropic) structures with strong interlayer interaction. One of the important physical examples of nonlinear modes in such structures is the so-called supersolitons, localized excitations of the density of a vortex lattice propagating in a system of interacting (parallel) long Josephson junctions. We show that the dynamics of these structures may be described by the so-called sine-lattice (SL) equation first introduced by S. Takeno and S. Homma [J. Phys. Soc. Jpn. 55 (1986) 65] and its various generalizations, e.g. those which include a transverse degree of freedom or more general types of the interlayer (nonlinear) interactions described by periodic Jacobi elliptic functions. We analyze nonlinear localized waves in such generalized SL equations analytically and numerically, and show that, in general, density waves may be of three types, namely kinks, dynamical solitons, and envelope solitons. We investigate also the transverse stability of quasi-one-dimensional solitons in the framework of the effective modified Boussinesq equation valid for both small amplitudes and continuous approximation, as well as investigate numerically the effects of perturbations (dissipation or point-like impurities) on the dynamics of π -kinks.