Study on solitary wave solutions of nonlinear evolution equations

Abstract

This research is devoted to study of two analytical methods for finding the solitary wave solutions of nonlinear evolution equations those arise in mathematical physics and engineering fields. Here we have discussed the main steps of two methods: the improved Kudryashov method and the generalized ODE method. In our research work, we have also used these two methods for finding exact and then solitary wave solutions and their respective graphs of Korteweg de-Vries (KdV) equation, modified Liouville equation, the (2+1)-dimensional Boussinesq-Kadomtsev-Petviashvili equation and regularized long wave equation. Finally, we have represented the results and comparative discussion between present and studied methods through the obtained solutions of the above equations. It has been established that the studied methods offer a further influential mathematical tool for constructing solitary wave solutions of nonlinear evolution equations in mathematical physics.