A symbolic computational method for constructing exact solutions to difference-differential equations

In this paper, we extended tanh method to solve difference-differential equations and pure difference equations with the projective Riccati equation. As an example, we applied this method to a (2 + 1)-dimensional Toda lattice equation. As a result, many exact solutions are obtained with the help of symbolic system Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equations.