构造非线性微分差分方程精确解的一种方法

A Method of Constructing the Exact Solutions to Nonlinear Differential-difference Equations

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.

In this letter,an algorithm is devised for using the G＇/G-expansion mett：oa 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 ra- tional function solutions with parameters are obtained. When the parameters are taken as spe- cial values, some known solutions including kink-type solitary wave solution, singular travel- ling 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-differ- ence equations in mathematical physics.