Multiplicity of vortex soliton families in the discrete Ginzburg-Landau equation, their interactions and the formation of bound states

TL;DR

This paper explores the coexistence and interactions of multiple stable vortex soliton families in the discrete cubic-quintic complex Ginzburg-Landau equation, revealing bound states and their persistence in the conservative limit.

Contribution

It uncovers a broad parameter space with multiple stable vortex soliton families and their bound states, using continuation methods.

Findings

Multiple stable vortex soliton families coexist in the parameter space.

Bound states of vortex solitons are dynamically formed and stable.

These structures persist in the conservative limit at high power.

Abstract

By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions have a symmetric amplitude profile and two different topological charges. We also discover the dynamical formation of a variety of 'bound-state' solutions, composed of two or more of these vortex solitons. All of these stable composite structures persist in the conservative cubic limit, for high values of their power content.