Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations

The Jacobi elliptic function expansion method is extended to derive theexplicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples arechosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobielliptic cosine function and the third elliptic function solutionsare obtained. It is shown that the shock wave solutions andsolitary wave solutions can be obtained at their limit condition.