Vortex solitons of the discrete Ginzburg-Landau equation

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 for two different closed loops encircling, i.e., centered at, the singularity. Their regions of existence and stability are determined. Additionally, we have analyzed the relationship between dissipation and stability for a number of solutions, finding that dissipation favors the stability of the vortex soliton solutions.