New rational formal solutions for (1Â +Â 1)-dimensional Toda equation and another Toda equation

In this paper, we present a new rational expansion method to uniformly construct a series of exact solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some well-known solutions, but also finds some new and general solutions. The efficiency of the method can be demonstrated on (1 + 1)-dimensional Toda equation and another Toda equation.