利用G′/G展开法构造非线性微分差分方程的精确解

The G′/G-expansion Method and Solutions of 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非线性微分差分Schr dinger方程和DCCGL方程的3类涉及任意参数的精确解,当这些参数取特殊值时,可得这2个方程的钟状孤立波解、扭状孤立波解以及三角函数解等.研究结果表明,该方法是探讨非线性微分差分方程精确解的一个有效而简洁的算法.

In this paper,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 nonlinear differential difference equations,Schrdinger equation and DCCGL equation,to illustrate the validity and advantages of the algorithm.As a result,hyperbolic function solutions and trigonometric function solutions with parameters are obtained.When the parameters are taken as special values,some known solutions including kink-type solitary wave solution 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.