Explicit Analytic Solution for the Nonlinear Evolution Equations using the Simplest Equation Method

In this paper, we focus on the exact solution of the coupled nonlinear Schrödinger type equation by means of the simplest equation method for the cases when the simplest equation is the equation of Bernoulli or the equation of Riccati. We use the appropriate ansätz to convert the above-mentioned equations to an ordinary differential equation and reduced to nonlinear algebraic systems of relationships among the parameters of the equations and the parameters of the solution. The method used here can be also extended to many other nonlinear partial differential equations. The properties of some solutions for this system are shown by some figures.