Investigating the nonlinear dynamics of acoustic waves by analyzing the Kadomtsev–Petviashvili equation in an unmagnetized plasma

This study explores the bifurcation analysis of ion-acoustic (IA) waves, electrostatic IA soliton propagation, as well as the behavior of periodic waves and chaos in a three-component, unmagnetized plasma composed of fully ionized ions and (r, q)-distributed electrons and positrons. To investigate the nonlinear behavior of IA waves across different plasma parameters, the Kadomtsev–Petviashvili equation is derived using the well-known reductive perturbation method. By applying a traveling wave transformation, a planar dynamical system is formulated. The phase portrait is then constructed to provide a detailed examination of the nonlinear wave phenomena emerging in the system. In addition, the Lyapunov spectrum is analyzed to determine whether the system exhibits chaotic motion. The impact of physical parameters on both the electrostatic and Sagdeev potentials is also studied. The findings of this research could contribute significantly to advancing the understanding of soliton propagation physics in astrophysical settings, various plasma environments, and laboratory experiments.