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The \((\frac{G'}{G})\)-expansion method for nonlinear differential-difference equations. (English) Zbl 1228.34096

Summary: In this Letter, an algorithm is devised for using the \((\frac{G'}{G})\)-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 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.

MSC:

34K05 General theory of functional-differential equations
34K31 Lattice functional-differential equations
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