Abundant Jacobi elliptic function solutions of nonlinear evolution equations

Abstract

In this paper, the twelve Jacobi elliptic functions are divided into four groups, and a new general Jacobi elliptic function expansion method is proposed to construct abundant doubly periodic Jacobi elliptic function solutions of nonlinear evolution equations. By this method, many exact doubly periodic solutions are obtained which shows the powerfulness of this method. When the modulus m→1 or 0, these solutions degenerate to the corresponding solitary wave solutions, shock wave solutions or trigonometric function (singly periodic) solutions.