Solitary wave analysis of the Kadomtsev–Petviashvili model in mathematical physics

Abstract

The (3 + 1)-dimensional Kadomtsev–Petviashvili equation has significant applications that emerge in the study of fluids and multi-component plasmas. The main object of our study is to investigate stable and efficient solitary solutions to the stated wave equations through two different schemes that provide generic solutions like exponential functions, trigonometric functions, hyperbolic functions, etc. The graphical illustrations for different values of the corresponding parameters of the attained solutions are explained in order to expose the intimate structure of the substantial phenomena. In particular, changes in wave position and category with respect to time are deliberated extensively through 2D figures. It has been found that wave velocity depends on some free parameters associated with the methods used to solve the equation. It has been demonstrated that for different values of the free parameters, the obtained solutions of the KP model exhibit dark soliton, peakon shape soliton, dark soliton-type wave, bright soliton, bell-shaped soliton, etc. Moreover, the direction and position of the solitons for the variation of other parameters are measured, from which a simple and comprehensive interpretation of the various aspects of water waves can be obtained. We think the obtained solution could be highly useful for studying nonlinear events in fluid dynamics, wind waves, and wind-generated waves.