Stochastic averaging principle for multiscale stochastic linearly coupled complex cubic-quintic Ginzburg-Landau equations

TL;DR

This paper establishes an averaging principle for multiscale stochastic coupled complex Ginzburg-Landau equations, enabling reduction to a single equation with modified coefficients, facilitating analysis of systems with different time scales.

Contribution

It introduces a novel averaging principle for multiscale stochastic coupled Ginzburg-Landau equations, reducing complexity by eliminating fast variables under certain conditions.

Findings

Existence of an averaging equation for the coupled system.

Reduction of the multiscale system to a single stochastic Ginzburg-Landau equation.

Conditions under which the averaging principle holds.

Abstract

Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. In this paper, we will establish an averaging principle for multiscale stochastic linearly coupled complex cubic-quintic Ginzburg-Landau equations with slow and fast time scales. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for this coupled system is proved, and as a consequence, the system can be reduced to a single stochastic complex cubic-quintic Ginzburg-Landau equation with a modified coefficient.