Perturbation-induced radiation by the Ablowitz-Ladik soliton

Solitons in strongly driven discrete nonlinear Schrödinger-type models

Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear Schrödinger (DNLS) equations with damping and strong rapid drive are investigated. The averaged equations have the forms of the parametric AL and DNLS equations. An additional type of parametric bright discrete soliton and cnoidal waves are found and the stability properties are analyzed. The analytical predictions of the perturbed inverse scattering transform are confirmed by the numerical simulations of the AL and DNLS equations with rapidly varying drive and damping.

Dynamics of the Ablowitz-Ladik soliton train

It is shown that dynamics of a train of N weakly interacting Ablowitz-Ladik solitons with (almost) equal velocities and masses is governed by the complex Toda chain model. The integrability of the complex Toda chain model provides the means to describe analytically various dynamical regimes of the N-soliton train and to predict initial soliton parameters responsible for each of the regimes. Numerical simulations corroborate well analytical predictions. A specific feature arising for the discrete soliton train system is the appearance of an additional (with respect to the lattice spacing) spatial scale-intersoliton distance. We comment on interplay between both spatial scales.