A generalized coth-function method for exact solution of differential–difference equation

In this paper we propose a new algebraic algorithm to compute the exact travelling wave solutions of nonlinear differential–difference equations. The idea of the proposed algorithm is generated from generalizing the hyperbolic cotangent (coth-) function. Numerical examples are given to illustrate the efficiency and effectiveness of the proposed method. It has been shown that new types of exact travelling wave solutions for these nonlinear differential–difference equations can be constructed.