Analytic solutions to nonlinear differential-difference equations by means of the extended (G′/G)-expansion method

In this paper, a discrete extension of the (G /G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schrdinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising.