Exact travelling wave solutions of the discrete sine-Gordon equation obtained via the exp-function method

In this paper, we generalize the exp-function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations, to nonlinear differential-difference equations (NDDEs). As an illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the exp-function method. As some special examples, these new exact travelling wave solutions can degenerate into the kink-type solitary wave solutions reported in the open literature. (C) 2007 Elsevier Ltd. All rights reserved.