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 31 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 PDF BibTeX XML Cite \textit{S. Zhang} et al., Phys. Lett., A 373, No. 10, 905--910 (2009; Zbl 1228.34096) Full Text: DOI OpenURL References: [1] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering, (1991), Cambridge Univ. Press New York · Zbl 0762.35001 [2] Hirota, R., Phys. rev. lett., 27, 1192, (1971) [3] Miurs, M.R., Backlund transformation, (1978), Springer Berlin [4] Weiss, J.; Tabor, M.; Carnevale, G., J. math. phys., 24, 522, (1983) [5] Yan, C.T., Phys. lett. A, 224, 77, (1996) [6] Wang, M.L., Phys. lett. A, 213, 279, (1996) [7] El-Shahed, M., Int. J. nonlinear sci. numer. simul., 6, 163, (2005) [8] He, J.H., Int. 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