Soliton Solutions to the BA Model and (3 + 1)-Dimensional KP Equation Using Advanced exp − ϕ ξ -Expansion Scheme in Mathematical Physics

Abstract

In this manuscript, the primary motivation is the implementation of the advanced $\text{exp}\left(-\varphi \left(\xi \right)\right)$ -expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Here, the solutions’ behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced $\text{exp}\left(-\varphi \left(\xi \right)\right)$ -expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced $\text{exp}\left(-\varphi \left(\xi \right)\right)$ -expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences.