Unraveling the (4+1)-dimensional Davey-Stewartson-KadomtsevPetviashvili equation: Exploring soliton solutions via multiple techniques

The (4+1)-dimensional Davey-Stewartson-Kadomtsev-Petviashvili equation is explored in the present work, revealing its complex dynamics and solitary wave solutions. Modeling ocean and tidal waves, particularly tsunami and long water waves, depends significantly on this nonlinear equation. Additionally, these models can be used to simulate internal and external waves in rivers and oceans as well as wave packets in water with a finite depth. The Sardar subequation method, new Kudryashov's method, and (1/v(zeta),v '(zeta)/v(zeta)) method are investigated to discover novel solitary wave solutions in the terms of hyperbolic, trigonometric and rational functions. A wide variety of solitons, as dark, bright, periodic, singular, combined dark-singular solitons and, combined dark-bright are obtained by these techniques. By taking accurate parameter values, certain three-dimensional and two-dimensional graphs are plotted to improve the physical description of solutions. The intriguing field of nonlinear waves and dynamic systems is signaled to readers by this work, which suggests a major advancement in understanding the intricate and unexpected behavior of this model.