Two-dimensional structures in the quintic Ginzburg-Landau equation

TL;DR

This study uses extensive numerical simulations to explore the existence and stability of various two-dimensional dissipative solitons in the complex Ginzburg-Landau equation with cubic and quintic nonlinearities, revealing new soliton classes.

Contribution

The paper introduces two novel classes of dissipative solitons in the 2D complex Ginzburg-Landau equation and maps their existence regimes through detailed numerical simulations.

Findings

Identified eight classes of dissipative solitons, including six known and two new types.

Mapped the parameter ranges for stable and unstable soliton structures.

Discovered richer behaviors by varying initial conditions and vorticity.

Abstract

By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find the range of existence of the spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation with cubic and quintic nonlinearities. We start from the parameters used by Akhmediev {\it et. al.} and slowly vary them one by one to determine the regimes where solitons exist as stable/unstable structures. We present eight classes of dissipative solitons from which six are known (stationary, pulsating, vortex spinning, filament, exploding, creeping) and two are novel (creeping-vortex propellers and spinning "bean-shaped" solitons). By running lengthy simulations for the different parameters of the equation, we find ranges of existence of stable structures (stationary, pulsating, circular vortex spinning, organized exploding), and unstable structures (elliptic vortex spinning that leads to filament, disorganized exploding, creeping). Moreover, by varying even the two initial conditions together with vorticity, we find a richer behavior in the form of creeping-vortex propellers, and spinning "bean-shaped" solitons. Each class differentiates from the other by distinctive features of their energy evolution, shape of initial conditions, as well as domain of existence of parameters.