Journal of Applied Mathematics
Volume 2012 (2012), Article ID 427479, 30 pages
http://dx.doi.org/10.1155/2012/427479
Research Article

The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations

Khaled A. Gepreel,1,2 Taher A. Nofal,2,3 and Ali A. Al-Thobaiti2

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

Received 21 March 2012; Accepted 30 May 2012

Academic Editor: Jianke Yang

Copyright © 2012 Khaled A. Gepreel et al. 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 modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.