On the integrability, multi-shocks, high-order kinky-breathers, L-lump–kink solutions for the non-autonomous perturbed potential Kadomtsev–Petviashvili equation

• Published in: Nonlinear dynamics Vol. 112; no. 15; pp. 13335 - 13359
• Main Authors: Alhejaili, Weaam, Roy, Subrata, Raut, Santanu, Roy, Ashim, Salas, Alvaro H., Aboelenen, Tarek, El-Tantawy, S. A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2024; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Dynamical Systems; Engineering; Fluid dynamics; Lie groups; Mathematics; Mechanical Engineering; Physics; Plasma physics; Solution space; Topography; Vibration; Shock waves; Potential Kadomtsev–Petviashvili equation; Kinky-breather waves; Lump–kink waves; Lax pairs; Bäcklund transformation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-09707-4

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.