Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations

In this paper, an algorithm is presented to find exact polynomial solutions of nonlinear differential-difference equations(DDEs) in terms of the Jacobi elliptic functions. The key steps of the algorithm are illustrated by the discretized mKdV lattice. A Maple package JACOBI is developed based on the algorithm to automatically compute special solutions of nonlinear DDEs. The effectiveness of the package is demonstrated by applying it to a variety of equations.