Discrete Solitons of the Ginzburg-Landau Equation

Abstract

In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear properties, the existence of self-localized dissipative solitons in the presence of cubic-quintic terms and modulational instability induced by saturable nonlinearities. Dynamical stability properties of localized and extended dissipative discrete solitons are also discussed.

arXiv commentChapter 11 of the book "Dissipative Optical Solitons" (Mario F.S. Ferreira, Editor), Springer, 2021