Exact Travelling Wave Solutions for Stochastic Fractional Hirota-Satsuma Coupled KdV Equations

Abstract

A modied fractional sub-equation method is used for constructing exact travelling wave solutions of nonlinear stochastic fractional partial dierential equations. The main idea of this method is to take full advantage of the fractional Riccati equation, which has many exact solutions. Moreover, white noise functional solutions are obtained for the Wick-type stochastic fractional Hirota-Satsuma coupled KdV equations via Hermite transform and white noise analysis. These solutions include stochastic exponential decay, soliton, and periodic wave solutions.