Rational expansion method of exponent function for solving exact   solutions to nonlinear differential-difference equations
  A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some examples are dealt with and their abundant exact solutions which include solitary solutions and periodic solutions are obtained. Among them, many solutions are new. 
Chengshi Liu