A modified hyperbolic function method and its application to the Toda lattice

In this paper, based on the computer symbolic system––Maple, we presented a modified hyperbolic function method to search for the exact solutions of nonlinear differential-difference equations (DDEs). The discrete Toda lattice is chosen to illustrate the method, and abundant new exact solutions are obtained, which include kink-shaped solitary wave solutions and other new types of exact solutions. This method can also be applied to many other nonlinear differential-difference equations (DDEs) in mathematics physics.