Exact and explicit solutions for the discrete Burgers equation by means of the Exp-function method

In recent years, various direct methods were proposed to find exact solutions not only for nonlinear partial differential equations but also for nonlinear differential-difference equations (NDDEs). In this paper, the Exp-function method was extended to the discrete Burgers equation for searching traveling waves in closed forms. It was shown that the equation supported discrete solitary wave solutions. Our results, as test problems, might be of great importance for those who study in the field of numerical analysis. It can be concluded that the Exp-function approach provides a direct and efficient way to construct generic exponential wave solutions to NDDEs.