KP, MKP and G-KP soliton and overtaking collision among multi-soliton propagation in an unmagnetized (2 + 1)-dimensional collisionless plasma environment

This work investigates nonlinear wave dynamics in a (2 + 1)-dimensional plasma using the Kadomtsev–Petviashvili equation (KPE) and its extensions—the modified KPE (MKPE) and Gardner KPE (G-KPE). These equations are derived via the reductive perturbation technique to study multi-soliton interactions, with particular focus on overtaking collisions, which remain under explored. Soliton and multi-soliton solutions are obtained using the Hirota bilinear method. The results demonstrate that solitons preserve their structure post-collision, while their amplitude and width are significantly affected by plasma parameters such as ion streaming velocity, temperature and density ratios, and strength of nonextensivity and population of nonthermality. These findings enhance the understanding of nonlinear wave behavior in astrophysical and space plasma environments.