Numerical Simulations of Snake Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation

TL;DR

This paper explores novel dissipative soliton solutions in the complex cubic-quintic Ginzburg-Landau equation through numerical simulations and theoretical analysis, revealing five new classes of pulse solutions and analyzing their behavior.

Contribution

It introduces five new classes of dissipative solitons in the CCQGLE and develops a variational and dynamical systems framework to analyze their structure and behavior.

Findings

Discovery of five novel dissipative soliton classes

Development of a variational approximation for snaking solitons

Numerical analysis of soliton dynamics and structure

Abstract

Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation and (b) a system of three ordinary differential equations resulting from the variational approximation.