Higher Dimensional Kadomtsev–Petviashvili Equation: New Collision Phenomena

Abstract

This article analyzes the dynamics of waves to a new higher dimensional Kadomtsev−Petviashvili equation. The higher dimensional Kadomtsev−Petviashvili equation and its expansions have attracted a great deal of scientific interest during the past few decades. Several nonlinear phenomena in a range of domains, like the dynamics of long waves with modest amplitudes in oceans and plasma physics, are studied using this family. In this study, we successfully apply the Hirota bilinear method with the adoption of several test strategies. A set of results like breather, two-wave, and lump periodic solutions are secured. To visually depict the output, a variety of graphs featuring distinct shapes are produced in response to appropriate parameter values. The computational complexities and results emphasize the transparency, effectiveness, and ease of the technique, indicating the method’s applicability to many kinds of both static and dynamic nonlinear equations regarding evolutionary phenomena in computational physics, as well as other practical domains and research fields.