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