Diversity of wave structures to the conformable fractional dynamical model

This manuscript examines the recently developed conformable three-dimensional Wazwaz-Benjamin- Bona-Mahony (3D-WBBM) equation's dynamical behavior in terms of its spatial and temporal variables. The governing equation is stretch for the Korteweg-de-Vries equation that represents the unidirectional propagation of small amplitude long waves on the surface of hydro magnetic and acoustic waves in a channel, especially for shallow water. Solitary wave solutions of various types, such as kink and shock, as well as singleton, combined solitons, and complex solitons, are all retrieved. Additionally, solutions to hyperbolic, exponential, and trigonometric functions are obtained through the use of recently developed methods, namely the Kudryashov method (KM), the modified Kudryashov method (MKM), and the new extended direct algebraic method (NEDAM). The study conducts a comparison of our findings to wellknown findings, and concludes that the solutions reached here are novel. Additionally, the earned results are sketched in different shapes to demonstrate their dynamics as a function of parameter selection. We can assert from the obtained results that the applied techniques are simple, vibrant, and quite well, and will be helpful tool for addressing more highly nonlinear issues in various of fields, especially in ocean and coastal engineering. Furthermore, our findings are first step toward understanding the structure and physical behavior of complicated structures. We anticipate that our results will be highly valuable in better understanding the waves that occur in the ocean. We feel that this work is timely and will be of interest to a wide spectrum of experts working on ocean engineering models.(c) 2022 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

This manuscript examines the dynamical behavior of the recently developed conformable three-dimensional Wazwaz-Benjamin-Bona-Mahony equation in terms of its spatial and temporal variables. Various types of solitary wave solutions are obtained using different methods and compared to existing findings, concluding that the solutions obtained in this study are novel. The study also demonstrates the dynamics of the results and highlights the simplicity, flexibility, and effectiveness of the applied techniques in addressing highly nonlinear issues in ocean and coastal engineering.