Extended Riccati Equation Rational Expansion Method and Its Applicationto Nonlinear Stochastic Evolution Equations

Abstract

In this work, by means of a newmore general ansätz and the symbolic computation systemMaple, we extend the Riccati equation rational expansion method[Chaos, Solitons & Fractals 25 (2005) 1019] touniformly construct a series of stochastic nontravelling wavesolutions for nonlinear stochastic evolution equation. To illustratethe effectiveness of our method, we take the stochastic mKdVequation as an example, and successfully construct some new and moregeneral solutions including a series of rational formal nontravelingwave and coefficient functions' soliton-like solutions andtrigonometric-like function solutions. The method can also beapplied to solve other nonlinear stochastic evolution equation or equations.