Stratonovich–Khasminskii averaging principle for multiscale random Korteweg–de Vries-Burgers equation

Abstract

Abstract In this paper, we consider the multiscale random Korteweg–de Vries-Burgers (KdVB) equation, namely, the KdVB equation perturbated by a fast time oscillating external force and a random oscillating noise, the random oscillating noise is made up of a family of strong mixing stationary processes with singular small parameters. A Stratonovich–Khasminskii type averaging principle for multiscale random KdVB equation is established, in physics, this averaging principle can describe the asymptotic behavior for the propagation of small-amplitude long waves in nonlinear dispersive and dissipative media with singular structure and the soliton propagation in the random weakly viscous media or in the random field.