Exact Traveling Wave Solutions for the Non-Linear Couple Drinfel’d-Sokolov-Wilson (Dsw) Dynamical System Using Extended Jacobi Elliptic Function Expansion Method

Abstract

The study of water waves is significant for researchers working in many branches of science. The behaviour of waves can be studied by observation or experimental means, but theoretically, mathematical modeling provides solutions to many problems in physics and engineering. Progress in this field is inevitable, with those who work in mathematics, physics, and engineering putting forth interdisciplinary studies.
 
 Jacobi elliptic functions are valuable mathematical tools that can be applied to various aspects of mathematics, physics, and ocean engineering. In this study, traveling wave solutions of the general Drinfel'd-Sokolov-Wilson (DSW) system, introduced as a model of water waves, were obtained by using Jacobi elliptic functions and the wave dynamics were examined. The extended Jacobi elliptic function expansion method is an effective method for generating periodic solutions. It has been observed that the periodic solutions obtained by using Jacobi elliptic function expansions containing different Jacobi elliptic functions may be different and some new periodic solutions can be obtained. 3D simulations were made using MapleTM to see the behaviour of the solutions obtained for different appropriate values of the parameters. 2D simulations are presented for easy observation of wave motion. In addition, we transformed the one of the exact solutions found by the extended Jacobi elliptic function expansion method into the new solution under the symmetry transformation.