Discrete Solitons of the Ginzburg-Landau Equation
Mario Salerno, Fatkhulla Kh. Abdullaev
TL;DR
This paper reviews recent findings on localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation, focusing on soliton existence, diffraction effects, and stability properties.
Contribution
It provides a comprehensive overview of the existence, dynamics, and stability of dissipative solitons in the discrete Ginzburg-Landau equation, including effects of nonlinearities.
Findings
Existence of self-localized dissipative solitons with cubic-quintic terms
Analysis of modulational instability due to saturable nonlinearities
Discussion of stability properties of localized and extended solutions
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.
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Taxonomy
TopicsAdvanced Fiber Laser Technologies · Nonlinear Photonic Systems · Nonlinear Dynamics and Pattern Formation