Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 158142, 8 pages
doi:10.1155/2009/158142
Application of symbolic computation in nonlinear differential-difference equations
Fuding Xie1
, Zhen Wang2
and Min Ji1
1Department of Computer Science, Liaoning Normal University, Liaoning, Dalian 116081, China
2School of Physics and Electronic Technology, Liaoning Normal University, Liaoning, Dalian 116029, China
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.