Nonlinear models in ocean engineering: Exact solutions and 3D simulations of the general Drinfiel’d-Sokolov-Wilson system with Jacobi elliptic functions

Abstract

This interdisciplinary study highlights the crucial role of mathematics and physics in ocean engineering. In this study, the traveling wave solutions of the general Drinfiel’d-Sokolov-Wilson (DSW)-system, which was introduced as a model of water waves, were investigated. Converting the DSW-system to a more straightforward system of ordinary differential equation system with wave transform is the first step in the process. The solutions of the system were obtained using five different methods. These methods are effective methods for generating periodic solutions. It has also been seen that the periodic solutions we got using the Jacobi elliptic function expansions containing different Jacobi elliptic functions might be different, and that we can get some new periodic solutions. Given 3-dimensional simulations using Maple were made to see the behaviour of the solutions obtained for the appropriate different values of the parameters. This study is very important as it is the unique study in the literature in which five different Jacobi elliptic function expansion methods are discussed together. Jacobi elliptic functions are valuable mathematical tools that can be applied to various aspects of ocean engineering. Their use helps engineers better understand and predict the behaviour of waves, tidal forces, and other phenomena, ultimately leading to safer and more efficient structures and systems. The stability property of the obtained solutions was tested to demonstrate the ability of the obtained solutions.

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

“…Therefore, although the solutions we obtained structurally resemble each other, it is observed that different solutions emerge when looking at the hyperbolic function variables they contain. Additionaly it is seen that the solutions ( 16) and ( 18) obtained in this study coincide with the solutions obtained using the Jacobi elliptic function expansion method of the same system [20]. According to our research, other solutions obtained are not available in the literature.…”