Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 158142, 8 pages
doi:10.1155/2009/158142
Research Article

Application of Symbolic Computation in Nonlinear Differential-Difference Equations

Fuding Xie,1,2 Zhen Wang,3 and Min Ji1

1Department of Computer Science, Liaoning Normal University, Liaoning, Dalian 116081, China
2Key Laboratory of Mathematics and Mechanization (KLMM), Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, China
3School of Physics and Electronic Technology, Liaoning Normal University, Liaoning, Dalian 116029, China

Received 18 March 2009; Accepted 12 September 2009

Academic Editor: Yong Zhou

Copyright © 2009 Fuding Xie 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

A method is proposed to construct closed-form solutions of nonlinear differential-difference equations. For the variety of nonlinearities, this method only deals with such equations which are written in polynomials in function and its derivative. Some closed-form solutions of Hybrid lattice, Discrete mKdV lattice, and modified Volterra lattice are obtained by using the proposed method. The travelling wave solutions of nonlinear differential-difference equations in polynomial in function tanh are included in these solutions. This implies that the proposed method is more powerful than the one introduced by Baldwin et al. The results obtained in this paper show the validity of the proposal.