Solitary wave solutions to two nonlinear evolution equations via the modified simple equation method

Abstract

In this article, we investigate two essential nonlinear evolution equations namely modified dispersive water wave equations and the Whitham-Broer-Kaup model for dispersive long waves in the shallow water small-amplitude regime by using the modified simple equation (MSE) method. The obtained solutions with parameters expose that the method is incredibly prominent and effective mathematical tool for solving nonlinear evolution equations (NLEEs) in mathematical physics, applied mathematics and engineering. When the parameters have taken special values the solitary wave solutions are attained from the exact solutions. In addition, this procedure reduces the size of calculations.