This article demonstrates the integrability of the \((3+1)\) -dimensional non-autonomous perturbed potential Kadomtsev–Petviashvili (NpPKP) equation through lax pairs and Bäcklund transformation. Hirota’s bilinear form is used to build the multi-shock solutions, and the multi-kinky-breather solutions are studied analytically by looking at the vector choices in the solution space. The first-order kinky-breather and the first-order lump solutions are investigated in a two-shock solution. The three-shock seed solution is used to explain how the one-order kinky-breather solution and the one-shock solution interact. Analytical analysis determines how the multi-shock solution interacts with the periodic and hyperbolic shocks, breathers, and lump solutions. Various non-autonomous hybrid solutions, such as shock lump–kink and shock kinky-breather, and their interactions are also shown. An illustration of the obtained solutions is shown using specific parameter values. These proposed solutions are expected to provide a comprehensive explanation for the inherent ambiguity surrounding certain enigmatic nonlinear events observed in the broader domain of fluid dynamics, with a specific emphasis on the specialized subject of plasma physics.
