Application of He's Exp-ftmction Method to the Stochastic mKdV Equation

With the help of Hermit transformation, it is firstly that the exp-fimction method is applied to solve nonlinear stochastic partial differential equations, and some new exact solutions of the stochastic mKdV equation in the white noise environment are obtained. It is shown that the exp-function method provides a straightforward and important mathematical tool for nonlinear stochastic partial differential equations in mathematical physics.

[1]  M. A. Abdou,et al.  NEW PERIODIC SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS USING EXP-FUNCTION METHOD , 2007 .

[2]  Qing Liu Uniformly constructing a series of exact solutions for (2 + 1)-dimensional stochastic Broer–Kaup system , 2008 .

[3]  Ahmet Boz,et al.  Exact Solutions for a Class of Nonlinear Partial Differential Equations using Exp-Function Method , 2007 .

[4]  Sheng Zhang,et al.  APPLICATION OF EXP-FUNCTION METHOD TO HIGH-DIMENSIONAL NONLINEAR EVOLUTION EQUATION , 2008 .

[5]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[6]  Jerzy Zabczyk,et al.  Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach , 2007 .

[7]  Ji-Huan He,et al.  Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method , 2007, Comput. Math. Appl..

[8]  C. Dai,et al.  Exact travelling wave solutions of the discrete sine–Gordon equation obtained via the exp-function method , 2009 .

[9]  Yong Chen,et al.  The stochastic soliton-like solutions of stochastic mKdV equations , 2005 .

[10]  Yingchao Xie Exact solutions for stochastic mKdV equations , 2004 .

[11]  Xin-Wei Zhou,et al.  Exp-function method to solve the nonlinear dispersive K(m,n) equations , 2008 .

[12]  S D Zhu,et al.  Exp-function Method for the Discrete mKdV Lattice , 2007 .

[13]  M. Wadati Deformation of solitons in random media , 1990 .

[14]  Ji-Huan He Homotopy Perturbation Method for Bifurcation of Nonlinear Problems , 2005 .

[15]  Miki Wadati Stochastic Korteweg-de Vries Equation , 1983 .

[16]  Sheng Zhang,et al.  Application of Exp-function method to a KdV equation with variable coefficients , 2007 .

[17]  S D Zhu,et al.  Exp-function Method for the Hybrid-Lattice System , 2007 .

[18]  Ji-Huan He AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING , 2008 .

[19]  Wang Qi,et al.  Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations , 2006 .