Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method

Abstract

The (3 + 1)-dimensional generalized shallow water equation is a significant mathematical framework for analyzing the dynamic behavior of waves in ocean physics. The purpose of this article is to investigate some more generic soliton solutions of the generalized shallow water-like model in three dimensions. The investigation is conducted utilizing the sophisticated mathematical methodology known as the double variables $(\varphi \prime /\varphi ,1/\varphi )$ expansion technique. With this approach, we produce new propagating wave solutions for this model in the form of hyperbolic, trigonometric, and rational functions. In addition, we offer two- and three-dimensional graphical representations to help visualize the intricate physical phenomena of the system. We have constructed many soliton solutions, such as kink shape soliton solutions, anti-bell shape solutions, single periodic solutions, singular soliton solutions, and anti-kink shape solutions for different values of the free parameters involved in the obtained solutions. These graphical representations are predicated on certain parameter selections, which facilitate the understanding of the complicated general behavior for this model. Through the presentation of new findings in the field of soliton solutions for the aforementioned equation, this paper offers fresh perspectives and highlights hitherto overlooked aspects of this fascinating mathematical challenge. The paper illuminates new results on soliton solutions with different geometrical structures for the given equation, revealing hitherto overlooked facets of this intriguing mathematical challenge.

Keywords:

• The (3 + 1)-dimensional generalized shallow water equation
• the double variables $(\varphi \prime /\varphi ,1/\varphi )$ expansion method
• analytical wave solutions

Disclosure statement

No potential conflict of interest was reported by the author(s).