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Indexed by:期刊论文

Date of Publication:2009-11-02

Journal:PHYSICS LETTERS A

Included Journals:SCIE、Scopus

Volume:373

Issue:45

Page Number:4142-4151

ISSN No.:0375-9601

Key Words:Differential-difference equation; Differential transform method; Generalized differential transform method; Differential transform-Pade approximation

Abstract:In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Pade technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation. (C) 2009 Published by Elsevier B.V.