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.