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Zhang, Sheng; Dong, Ling; Ba, Jin-Mei; Sun, Ying-Na

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

Phys. Lett., A 373, No. 10, 905-910 (2009).
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.

Cited in 30 Documents

MSC:

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

Keywords:

nonlinear differential-difference equations; \((\frac{G'}{G})\)-expansion method; hyperbolic function solutions; trigonometric function solutions
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\textit{S. Zhang} et al., Phys. Lett., A 373, No. 10, 905--910 (2009; Zbl 1228.34096)
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