Spatiotemporal two-dimensional solitons in the complex Ginzburg-Landau equation

TL;DR

This paper explores the formation and stability of spatiotemporal two-dimensional solitons in the complex Ginzburg-Landau equation with cubic and quintic nonlinearities, revealing various soliton behaviors including stationary, pulsating, exploding, and vortex structures.

Contribution

It introduces a numerical approach to analyze 2D solitons in the complex Ginzburg-Landau equation with asymmetry between space and time variables, identifying new stable vortex solitons.

Findings

Identified stationary, pulsating, and exploding 2D solitons.

Discovered stable vortex solitons due to nonlinear competition.

Used Fourier spectral method for efficient numerical simulations.

Abstract

We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a powerful Fourier spectral method, i.e., a Fourier spatial discretization and an explicit scheme for time differencing. Varying the system's parameters, and using different initial conditions, numerical simulations reveal 2D solitons in the form of stationary, pulsating and exploding solitons which possess very distinctive properties. For certain regions of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result of a competition between focusing nonlinearities and spreading while propagating through medium.