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论文类型：期刊论文

发表时间：2010-10-01

发表刊物：COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

收录刊物：SCIE、EI、Scopus

卷号：15

期号：10

页面范围：2791-2797

ISSN号：1007-5704

关键字：Exact solution; Differential-difference equation; Lattice equation

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.