Exploration of solitary wave solutions of highly nonlinear KDV–KP equation arise in water wave and stability analysis

Abstract

For intellectual curiosity, in this manuscript, we study the sixth-order highly nonlinear generalized Korteweg–de Vries–Kadomtsev–Petviashvili dynamical model. The Kadomtsev–Petviashvili equation is used in conjunction with the popular fifth-order KDV model. The objective of this study is twofold: Firstly, we formulated the two analytical methods, namely, the unified method and the auxiliary method, to derive the differential families of soliton solutions under different conditions that have never been studied before. The scientific community interested in wave phenomena will find these results useful in understanding the dynamics of nonlinear phenomena in wave theory, optics, engineering, and plasma physics. Secondly, we examine the stability analysis of the selected model. For better understanding, we plotted 2D, 3D, contours and density graphs of these acquired solutions. We anticipate that this work will be a significant step forward in the analysis of highly nonlinear models.