On the nonlinear difference-differential equations arising in physics

Abstract

Here, an extended discrete tanh function method with a computerized symbolic computation is used constructing a new exact travelling wave solutions of nonlinear differential difference equations of special interest in physics, namely, Hybrid equation, Toda lattice equation and Relativistic Toda lattice difference equations. As a result, we obtain many kinds of exact solutions which include soliton solutions, periodic solutions and rational solutions in a uniform way if solutions of these kinds exist. The method is straightforward and concise, and it can also be applied to other nonlinear difference differential equations in physics.