Characteristic of integrability of nonautonomous KP-modified KP equation and its qualitative studies: soliton, shock, periodic waves, breather, positons and soliton interactions

This article demonstrates the characteristic of integrability of the nonautonomous KP-mKP equation through Painlevé analysis, bilinear Bäcklund and lax pairs. The nonautonomous KP-mKP equation is converted into the Bell polynomial from which bilinear Bäcklund is constructed and lax pair of the said equation is generated. Further, multi-solitons, smooth positon, breather, and their interaction are fabricated using Hirota’s bilinear approach. Besides, a qualitative analysis of the nonautonomous KP-mKP equation using bifurcation theory is carried out. The deformation of the periodic to quasiperiodic orbit signifying instability of the said system due to damping is observed. Additionally, the external periodic force perturbs the nonautonomous system’s low- and high-energy orbits, resulting in a chaotic structure via the path of intermittency, implying the presence of turbulent flow.