NONLINEAR ACOUSTIC WAVE PHENOMENA IN MAGNETIZED COLLISIONLESS RELATIVISTIC PLASMAS

Abstract

The thesis investigates the nonlinear propagation of ion-acoustic solitons (IASs) within a

magnetized rotating relativistic plasma environment. This environment comprises relativistic

ion fluids and electrons following (α,q)-distributions, alongside positrons. Employing

the reductive perturbation technique, the study derives the Korteweg-de Vries equation

(KdVE) with quadratic nonlinearity. However, when the coefficient associated with this

nonlinearity approaches zero, the method encounters limitations. To address this challenge,

adjustments are made to the stretching coordinates, leading to a KdVE with cubic

nonlinearity, suitable for describing soliton propagation near critical values in these plasma

conditions. Furthermore, a KdVE with quartic nonlinearity is derived, relevant for supercritical

values of specific plasma parameters in relativistic plasmas.

Prior research has predominantly explored relativistic effects on soliton propagation through

expansions of Lorentz relativistic factors up to three terms. In contrast, this thesis extends

the consideration to more than ten terms to minimize truncation errors in modeling nonlinear

soliton propagation within these plasmas. The investigation reveals that the relativistic

streaming factor significantly alters the wave potential functions. Notably, the derived

KdVE equations indicate that quadratic nonlinearity supports both compressive and rarefactive

soliton propagations, while cubic and quartic nonlinearities exclusively support

compressive solitons in these plasma settings.

The study further examines how plasma parameters, with the inclusion of the relativistic

Lorentz factor up to eleven terms, influence the amplitude and width of IASs for the

first time. It finds that higher-order terms of the relativistic Lorentz factor and obliqueness

notably modify the propagation characteristics of IASs within this specific plasma environment.