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. 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.

7 pages, 11 figures

References in corpus (3)

• Asymmetric vortex solitons in nonlinear periodic lattices
• The variety of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses
• Dissipative vortex solitons in 2D-lattices

Cited by in corpus (8)

• Vortex solitons in quasi-phase-matched photonic crystals
• Pinned modes in lossy lattices with local gain and nonlinearity
• Pattern formation by kicked solitons in the two-dimensionnal Ginzburg-Landau medium with a transverse grating
• Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity
• Building patterns by traveling vortices and dipoles in periodic dissipative media
• Localized vortex beams in anisotropic Lieb lattices
• Dissipative localised structures for the complex Discrete Ginzburg-Landau equation
• Dynamics of nonlocal and local discrete Ginzburg-Landau equations: global attractors and their congruence