Vortex solitons of the discrete Ginzburg-Landau Equation

TL;DR

This paper reports the discovery and analysis of vortex soliton solutions in two-dimensional discrete dissipative systems modeled by the cubic-quintic complex Ginzburg-Landau equation, highlighting their stability and topological properties.

Contribution

It introduces new families of vortex soliton solutions, including symmetric and asymmetric types with multiple topological charges, and explores their stability influenced by dissipation.

Findings

Dissipation enhances the stability of vortex solitons.

Multiple families of vortex solutions with different topological charges are identified.

Regions of existence and stability are mapped for these solutions.

Abstract

We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have simultaneously two different topological charges. Their regions of existence and stability are determined. Additionally, we have analyzed the relation- ship between dissipation and stability for a number of solutions. We have obtained that dissipation favours the stability of the solutions.