Discrete dissipative solitons

Abstract

The existence of discrete dissipative solitons in a nonlinear lattice is studied. The Ablowitz-Ladik (AL) model with linear damping, nonlinear cubic amplification, quintic damping and complex second difference, representing the discrete analogue of a filter, is investigated. The parameters of the discrete dissipative soliton are calculated using a perturbation theory for the AL model. Analytic predictions are confirmed by numerical simulations of the AL model with non-conservative perturbations. We also discuss modulational instability (MI) in the discrete complex Ginzburg-Landau (DCGL) equation and the existence the exact localized solutions.