Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation

Weimin Zhang

doi:10.1155/2011/451420

Abstract

The extended Jacobi elliptic function expansion method is applied for Zakharov-Kuznetsov-modified equal-width (ZK-MEW) equation. With the aid of symbolic computation, we construct some new Jacobi elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular functional (singly periodic) solutions.

Highlights

It is one of the most important tasks to seek the exact solutions of nonlinear equation in the study of the nonlinear equations
Many powerful methods have been developed such as inverse scattering transformation 1, Backlund transformation 2, Hirota bilinear method 3, homogeneous balance method 4, extended tanh-function method 5, Jacobi elliptic function expansion method 6 and Ma’s transformed rational function method 7
We found some new solutions of Jacobi elliptic function type that were not obtained by the sine-cosine method, the extended tanh-method, the mapping method, and other methods

Summary

Introduction

It is one of the most important tasks to seek the exact solutions of nonlinear equation in the study of the nonlinear equations. 8 , an extended-tanh method is used to establish exact travelling wave solution of the Zakharov-Kuznetsov-modified equal-width ZK-MEW equation. An extended Jacobi elliptic function expansion method is employed to construct some new exact solutions of the Zakharov-Kuznetsov-modified equal-width ZK-MEW equation. In 9 , the ZK equation is solved by the sine-cosine and the tanh-function methods. The modified equal width MEW equation given by ut 3u2ux − βuxxt 0, 1.4 has been discussed in 11. In 13 , some exact solutions of the ZK-MEW equation 1.5 was obtained by using the tanh and sine-cosine methods. We will give some new solutions of Jacobi elliptic function type of ZK-MEW equation by using an extended Jacobi elliptic function method.

The Extended Jacobi Elliptic Function Expansion Method

ZK-MEW Equation

Notice that

Conclusions