Bilinear Backlund, Lax Pairs, Lump waves and Soliton interaction of (2+1)-dimensional non-autonomous Kadomtsev-Petviashvili equation

Abstract This article describes the the characteristic of integrability via Painleve analysis of the Kadomtsev-Petviashvili (KP) equation under the influence of an external force along with a damping. Introducing the Hirota's approach multi-soliton solution of the said equation is acquired in excited systems. Utilizing the obtained solutions, the interaction of solitary wave is observed with special care. It has been observed that Interactive autonomous solitons appear to remain in their original shape after collision. However, the non-autonomous soliton change their shape and directions after collision. The background from which the solitons rises, also significantly changes due to the action of external forces. Further, lump type soliton and some complicated mixed soliton are derived from the bilinear form of the said equation with the appropriate choice of polynomial functions. On the basis of the obtained mixed soliton, the interaction of the strip soliton and lump wave are graphically described. During the investigation of the interaction, fusion type situation is appeared. Finally, from the analytical results of the relevant motions, it is also confirmed that the velocity, maximum altitude and interacting natures of the wave quantities are all influenced by the damping and forcing terms. The interacting natures of the wave quantities are entirely investigated also from numerical understanding.