Averaging principle for stochastic Korteweg-de Vries equation

Averaging principle is a powerful tool for studying qualitative analysis of nonlinear dynamical systems. In this paper, we will establish an averaging principle for stochastic Korteweg-de Vries equation under a general averaging condition. With the help of this averaging principle, we can establish an effective approximation for the solution of stochastic Korteweg-de Vries equation, this can tell us the asymptotic behavior of the solution and make the interaction between nonlinearity, uncertainty and multiple scales more clear. In order to obtain this averaging principle, we need to establish the smoothing effect for the third order operator. (C) 2019 Elsevier Inc. All rights reserved.