多尺度随机线性耦合复五次Ginzburg-Landau方程的随机平均原理
Stochastic averaging principle for multiscale stochastic linearly coupled complex cubic-quintic Ginzburg-Landau equations
摘要：
随机平均原理是研究不同时标随机动力系统定性分析的有力工具。本文建立了具有慢、快时间尺度的多尺度随机线性耦合复五次Ginzburg-Landau方程的平均原理。在适当的条件下，证明了该耦合系统存在一个消去快变量的平均方程，从而将该系统化为一个带修正系数的随机复五次Ginzburg-Landau方程.
英文摘要：
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.
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