On the study of dynamical wave's nature to generalized (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation: application in the plasma and fluids

This work explores the generalized variable-coefficient (3+1)-dimensional Kadomtsev-Petviashvili equation, which surfaces in fluid and multi-component plasma research as an important application. Plasmas and fluids are currently attracting attention because of their capacity to facilitate a wide range of wave phenomena. A diversity of wave structures, including M-lump-like waves and multiple solitons are secured. Moreover, the various hybrid solutions are analyzed and discussed with the assistance of the Hirota bilinear method and the long wave technique. The mechanical features of solutions and collision-related aspects within a diversity of nonlinear systems are demonstrated by the results of this investigation. The extracted solutions are thoroughly analyzed to determine their physical significance. This is done by presenting a range of graphs that illustrate the dynamics of the solutions for specific parametric values. The reliability of the methods we have implemented is confirmed by our findings, which also indicate their potential for future use in identifying unique and varied solutions to nonlinear evolution equations experienced in the fields of engineering and mathematical physics.