Journal of Applied Mathematics
Volume 2012 (2012), Article ID 710375, 15 pages
http://dx.doi.org/10.1155/2012/710375
Research Article

Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Khaled A. Gepreel1,2 and A. R. Shehata3

1Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
2Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
3Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt

Received 4 October 2011; Revised 13 December 2011; Accepted 13 December 2011

Academic Editor: Pablo González-Vera

Copyright © 2012 Khaled A. Gepreel and A. R. Shehata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.