Soliton solutions to a wave equation using the (ϕ'/ϕ)– expansion method

This article aims to explore and examine general soliton solutions within the context of the generalized Benjamin-Bona-Mahony equation. This equation is a significant mathematical tool employed in the study of wave dynamics in ocean physics. In this paper, we investigate and generate new propagating soliton solutions for the above-mentioned equation using the (ϕ′/ϕ) − expansion method, an elegant mathematical approach. Rational, trigonometric, and hyperbolic functions are used to express these solutions. In order to provide a visual comprehension of the complex physical phenomena regulating the system, we additionally demonstrate graphics in two and three dimensions. The study explores a range of parameter configurations that yield distinct soliton solutions. By visually depicting these solutions based on specific parameter choices, a deeper comprehension of the system's complex behavior is achieved. The article sheds light on novel findings concerning soliton solutions for the mentioned equation, unveiling previously unnoticed aspects of this captivating mathematical problem.