Abstract
This manuscript employs an exact and explicit soliton solution of the Drinfel'd–Sokolov–Wilson (DSW) equation. The wave phenomena of the obtained solutions are applied to water wave mechanics, fluid dynamics, ocean engineering and science. The new auxiliary equation (NAE) method was not applied to the DSW model. As a result, we applied this model to construct a lot of analytic solutions in the expression of hyperbolic, trigonometric, and explicit functions that included free parameters. The obtained solutions are explained in some plots in three-dimensional (3D) and two-dimensional (2D) graphs in this paper, which also discusses the effect of the wave phenomena in 2D diagrams. However, we have made comparisons between our solution and other solutions in the previous literature. Therefore, it is revealed that the mentioned method may be a potential tool for creating new precise soliton solutions for various NLEEs, which play an important role in applied science and engineering.
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