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Zbl 1228.34096
Zhang, Sheng; Dong, Ling; Ba, Jin-Mei; Sun, Ying-Na
The $(\frac{G'}{G})$-expansion method for nonlinear differential-difference equations. (English)
[J] Phys. Lett., A 373, No. 10, 905-910 (2009). ISSN 0375-9601

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 2000:: *34K05 General theory of functional-differential equations
34K31

Keywords: nonlinear differential-difference equations; $(\frac{G'}{G})$-expansion method; hyperbolic function solutions; trigonometric function solutions

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