A method for constructing discrete exact solutions and application to quintic discrete nonlinear Schrödinger equation

In this paper, we present a method to solve nonlinear difference differential equation(s). We applied this method to quintic discrete nonlinear Schrödinger equation to illustrate this method. Many exact solutions are obtained with the help of 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 equation(s).