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

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.