The non-autonomous perturbed potential Kadomtsev-Petviashvili equation: its integrability, kinky-quasiperiodic, kink-like breather, lump-kink solutions with mixed backgrounds

The integrability of (2+1)-dimensional non-autonomous perturbed potential Kadomtsev-Petviashvili (NpPKP) problem has been demonstrated in this manuscript using Lax pairs and the B & auml;cklund transformation. The bilinear form of the NpPKP problem has been generated with the help of Hirota polynomial technique. Using test function and N-dimensional Riemann theta function, the kink-like breathers, lump-kink, interaction of lump and shock and the kinky quasiperiodic are explored analytically in light of the vector selections in the solution space. Outcomes of the solutions are plotted as illustration using particular values of the relevant parameters. These findings may aid in our understanding of intriguing physical events and mechanisms in potential systems.