A systematic method for solving differential-difference equations

被引：1

作者：

Zhang, Yufeng ^{[1
]}

Hon, Y. C. ^{[2
]}

Mei, Jianqin ^{[3
]}

机构：

[1] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Peoples R China

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[3] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2010年 / 15卷 / 10期

关键词：

Exact solution; Differential-difference equation; Lattice equation; PERIODIC-WAVE SOLUTIONS; ELLIPTIC FUNCTION SOLUTIONS; RATIONAL FORMAL SOLUTIONS; COUPLED KDV EQUATIONS; TANH-FUNCTION METHOD; SOLITON-SOLUTIONS; DARBOUX TRANSFORMATION; BURGERS-EQUATION; EXPANSION METHOD;

D O I：

10.1016/j.cnsns.2009.10.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A systematic method for searching travelling-wave solutions to differential-difference equations (DDEs) is proposed in the paper. First of all, we introduce Backlund 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. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2791 / 2797

页数：7

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