On the solitons, breathers, and positons and their interactions to the non-autonomous perturbed Gardner-KP equation via modified bilinear methods

This investigation examines the dynamical characteristics of various soliton-type solutions of the (2+1)-dimensional non-autonomous perturbed Gardner–Kadomtsev–Petviashvili (NAPGKP) equation. Using its bilinear form, multi-soliton solutions are derived through Hirota’s approach. Intensive study on soliton propagation, soliton interaction, and complex hybrid solutions are performed. Breathers are explored from a multi-soliton solution by selecting a suitable complex conjugate relation in the wave vector. The significant impact of different parameters on the characteristic line of the breather is examined. Along with the group velocity, the phase velocity of the breather is presented explicitly. Positon solution of higher order and the interaction of other waveforms are exhibited by selecting suitable values of parameters.