A systematic method for solving differential-difference equations

✍ Scribed by Yufeng Zhang; Y.C. Hon; Jianqin Mei

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 766 KB
• Volume: 15
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2009.10.019

✦ Synopsis

A systematic method for searching travelling-wave solutions to differential-difference equations (DDEs) is proposed in the paper. First of all, we introduce Bäcklund transformations for the standard Riccati equation which generate new exact solutions by using its simple and known solutions. Then we introduce a kind of formal polynomial solutions to DDEs and further determine the explicit forms by applying the balance principle. Finally, we work out exact solutions of the DDEs via substituting the form solutions and solving over-determined algebraic equations with the help of Maple. As illustrative examples, we obtain the travelling-wave solutions of the (2 + 1)-dimensional Toda lattice equation, the discrete modified KdV (mKdV) equation, respectively.