| 构造非线性微分差分方程精确解的一种方法 |
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| 引用本文： | 许丽萍.构造非线性微分差分方程精确解的一种方法[J].应用数学,2012,25(3):481-487. |
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| 作者姓名： | 许丽萍 |
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| 作者单位： | 河南科技大学数学与统计学院,河南洛阳,471003 |
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| 基金项目： | 河南省国际合作交流项目(084300510060,094300510050) |
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| 摘 要： | 把最近提出的G′/G展开法推广到了非线性微分差分方程,利用该方法成功构造了一种修正的Volterra链和Toda链的双曲函数、三角函数以及有理函数三类涉及任意参数的行波解,当这些参数取特殊值时,可得这两个方程的扭状孤立波解、奇异行波解以及三角函数状的周期波解等.研究结果表明,该算法探讨非线性微分差分方程精确解十分有效、简洁.
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| 关 键 词： | G′/G展开法 微分差分方程 精确解 |
A Method of Constructing the Exact Solutions to Nonlinear Differential-difference Equations |
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| XU Liping.A Method of Constructing the Exact Solutions to Nonlinear Differential-difference Equations[J].Mathematica Applicata,2012,25(3):481-487. |
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| Authors: | XU Liping |
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| Institution: | XU Liping (School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471003,China) |
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| Abstract: | In this letter,an algorithm is devised for using the G′/G-expansion method to solve nonlinear differential-difference equations.With the aid of symbolic computation,we choose two discrete nonlinear lattice equations to illustrate the validity and advantages of the algorithm.As a result,hyperbolic function solutions,trigonometric function solutions and rational function solutions with parameters are obtained.When the parameters are taken as special values,some known solutions including kink-type solitary wave solution,singular travelling wave solutions and singular travelling wave solution are recovered.It is shown that the proposed algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics. |
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| Keywords: | G′/G-expansion method Nonlinear differential-difference equation Exact solution |
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