Obtaining Solitary Solutions of Two Well-Known Systems Using a Coupled Modified Simplest Method

One of the topics of curiosity in recent years in miscellaneous sciences such as physics and engineering is to attain analytical answers to evolution equations. In this work, a novel modification of the simplest equation method has been suggested to solve the nonlinear system of the partial differential equation. As an example, the proposed methods have been applied to achieve the exact solutions of the coupled generalized Schrödinger–Boussinesq system and Boussinesq-type coupled system. By giving specific values to the parameters, private answers are obtained and the plots of solutions are drawn. The newly-used method is highly accurate, flexible, effective, and programmable to solve systems of differential equations.