Dynamics of Ion-Acoustic Soliton Propagation Near the Super-Critical Values in Relativistic Magnetized Plasmas

This article focuses the derivation of a new evolution equation with quartic nonlinearity and its analytical solution along with dynamical features for investigating nonlinear propagation characteristics of ion-acoustic soliton (IAS) in a magnetized, rotating, relativistic plasma environment comprising of relativistic ion fluids and generalized distributed electrons, and positions. Employing the conventional reductive perturbation method, the Korteweg-de Vries (KdV) equation involving quartic nonlinearity is derived. The effect of obliqueness, relativistic streaming factor, rotational frequency, and other related plasma parameters on the nonlinear propagation characteristic is analyzed. The plasma parameters affect remarkably the propagation characteristics of IASs with the consideration of relativistic Lorentz factor (RLF) up to 20 terms rather than 2 or 3 terms. Through the implementation of a traveling wave transformation, a planar dynamical system (PDS) is rigorously formulated. The phase portrait is meticulously constructed, allowing for a comprehensive and deeply nuanced analysis of the emergent nonlinear wave phenomena inherent to the system. It is observed that even the slightest alteration in any parameter can exert a significant and abrupt influence on the propagation dynamics of IASs when approaching the super-critical threshold. The findings presented may contribute to the underlying physics in understanding soliton propagation in the astrophysical scenarios such as magnetosphere, neutron stars, dark matter halos, white dwarfs, etc. in the presence of magnetic field.