The G′/G-expansion Method and Solutions of Nonlinear Differential-Difference Equations

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.