Spatiotemporal Dynamics, Stability and Interaction Mechanisms of Multidimensional Nonlinear Waves in Complex Physical Media

ABSTRACT In this study, the dynamic behaviors of the generalized (3 + )‐dimensional Kadomtsev‐Petviashvili equation, an important mathematical model for nonlinear wave propagation, are examined through interaction solutions. Using interaction solutions such as breather, two‐wave, and lump periodic solutions, the interactions between the solitary wave solutions of the equation and their dynamic characteristics are analyzed in detail. Then, advanced analytical solution methodologies, such as the Kumar‐Malik and the Sardar‐sub equation methods, are employed to obtain analytical solutions in the form of solitary waves. Thanks to these analytical methods, a variety of wave solutions, including Jacobi elliptic, dark, bright, kink, periodic, singular, and lump solitary waves, are also obtained. Moreover, to better understand the physical behaviors of the obtained results, 3D, 2D, and contour visualizations are demonstrated. These visualizations clearly illustrate the spatial and temporal evolution of the solitary wave solutions and the dynamics of the interactions. In addition, this study focuses on the stability analysis of the obtained solutions. Finally, approximate solutions found by the finite difference method and results compared with exact solutions and their graphics are obtained. The results of this research have numerous potential uses. Such as, they can be used in fields such as ferromagnetic materials, Bose‐Einstein condensates, hydrodynamics and fluid mechanics, ocean physics, and reaction‐diffusion equations. In plasma physics, the breather solutions and multi‐soliton interactions of the Kadomtsev‐Petviashvili equation play a significant role in understanding the interactions of energy‐carrying waves in plasmas. The methods used in this study are applied to the equation for the first time in the literature.