  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.
