Abstract and Applied Analysis
Volume 2013 (2013), Article ID 756896, 10 pages
http://dx.doi.org/10.1155/2013/756896
Research Article

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Khaled A. Gepreel,1,2 Taher A. Nofal,2,3 and Fawziah M. Alotaibi2

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

Received 24 July 2012; Revised 13 October 2012; Accepted 20 November 2012

Academic Editor: Patricia J. Y. Wong

Copyright © 2013 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 truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.