Explicit solitary solutions to the toda lattice equation

Abstract: A constructive method for exactly solving difference-difference equations(DDE) is presented, which is called the modified F-function method. In this method, the solution to DDEs is supposed to be a polynomial of the function F whereas F satisfies a general Riccati equation. By selecting proper coefficients of the Riccati equation, explicit solitary solutions of DDEs can be obtained. The Toda lattice equations is given as an example