A new algebraic procedure to construct exact solutions of nonlinear differential–difference equations

This paper presents a new algebraic procedure to construct exact solutions of selected nonlinear differential–difference equations. The discrete sine-Gordon equation and differential–difference asymmetric Nizhnik–Novikov–Veselov equations are chosen as examples to illustrate the efficiency and effectiveness of the new procedure, where various types of exact travelling wave solutions for these nonlinear differential–difference equations have been constructed. It is anticipated that the new procedure can also be used to produce solutions for other nonlinear differential–difference equations.