Abstract
In this article, we construct the traveling wave solutions involving parameters of the nonlinear differential difference equations via the lattice equation, the relativistic Toda lattice equations and the (1 + 1)-dimensional Toda equation in terms of the hyperbolic functions and trigonometric functions by using the improvement (G'/G)-expansion method, where G satisfies a discrete second order linear ordinary differential equation. When the parameters are taken special values, the solitary wave are derived from the traveling waves.