A Modification of the Generalized Kudryashov Method for the System of Some Nonlinear Evolution Equations

In this study, a comparatively new technique named the generalized Kudryashov method (gKM) has been effectively implemented to explore the exact traveling wave solutions to some nonlinear evolution equations (NLEEs) in the field of nonlinear science and engineering. The effectiveness of the new functional method has been demonstrated by investigating single as well as coupled equations with arbitrary parameters explicitly the coupled Higgs field equation, the Benney-Luke equation, and the Drinfel'd-Sokolov-Wilson (DSW) equation. As a matter of fact, the solution attained in this article thrust into the abundant wave solutions which includes kink, singular kink, periodic and solitary wave solutions. Moreover, the characteristics of these analytic solutions are interpreted depicting some 2D and 3D graph by using computer symbolic programming Wolfram Mathematica. The computational work ascertained that the employed method is sturdy, simple, precise, and wider applicable. Also, the prominent competence of this current method ensures that practically capable to reducing the size of the computational task and can be solved several nonlinear types of new complex higher order partial differential equations that originating in applied mathematics, computational physics and engineering.