Ion acoustic solitons and periodic waves with dynamical features around the supercritical values in relativistic unmagnetized plasmas

Abstract This study examines the nonlinear propagation and dynamic behavior of ion acoustic (IA) waves in unmagnetized relativistic plasmas (UMRP), consisting of relativistic warm ion fluids and Cairns-distributed inertialess electrons and positrons. Using the well-established reductive perturbation method, the quartic Korteweg–de Vries equation (KdVE) is derived with the existence of super-critical value to investigate the dynamical features and propagation characteristics of IA waves in such plasmas. Additionally, a traveling wave transformation is applied to develop a planar dynamical system, and its phase portrait is analyzed to gain insights into the nonlinear wave behavior. The impact of plasma parameters on the propagation and dynamic characteristics of IA waves is also explored. The findings reveal that plasma parameters have a substantial effect on the propagation properties of IA waves and their associated electric fields, particularly when the Lorentz relativistic factor (LRF) is expanded up to 20 terms, as opposed to the conventional two or three terms It is also observed that minor variations in any parameter can profoundly influence the bifurcation features and nonlinear propagation dynamics of IA wave at the super-critical value. These findings could contribute to a better understanding of solitary wave dynamics in astrophysical environments such as magnetospheres, neutron stars, dark matter halos, and white dwarfs, etc.