Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 158142, 8 pages
Application of Symbolic Computation in Nonlinear Differential-Difference Equations
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.
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.