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 well-known 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.