Soliton turbulences in the complex Ginzburg-Landau equation

TL;DR

This paper investigates soliton turbulence in the complex Ginzburg-Landau equation, revealing how parameter ratios influence pulse distributions and identifying a continuous family of turbulence states near integrability.

Contribution

It demonstrates the dependence of soliton pulse distributions on parameter ratios and uncovers a continuum of turbulence states close to the integrable nonlinear Schrödinger equation.

Findings

Pulse amplitude and wavenumber distributions depend only on parameter ratios.

Existence of a one-parameter family of soliton turbulence states.

Turbulent states are closely related to the nonlinear Schrödinger equation.

Abstract

We study spatio-temporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many soliton-like pulses appear in the parameter range, because the complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger equation. We find that the distributions of amplitude and wavenumber of pulses depend only on the ratio of the two parameters of the amplification and the viscosity. This implies that a one-parameter family of soliton turbulence states characterized by different distributions of the soliton parameters exists continuously around the completely integrable system.