NUMERICAL INVESTIGATIONOFNONLINEAR ACOUSTICWAVEPHENOMENA INSTRONGLYAND WEAKLYCOUPLEDPLASMAS

Abstract

This thesis investigates nonlinear acoustic wave phenomena in both strongly and weakly coupled collisionless unmagnetized plasmas using analytical and numerical methods. By developing mathematical models for different plasma environments, the study employs the reductive perturbation technique (RPT) to derive nonlinear evolution equations (NLEEs). These equations are then used to analyze the propagation of shock waves, solitons, and periodic waves in various plasma configurations. In Chapter 2, Burgers equations involving quadratic, cubic, and combined quadratic-cubic nonlinearities are derived for a coupled complex plasma system consisting of Boltzmann-distributed electrons, nonthermal ions, and charged dust particles. The generalized Riccati equation mapping method (GREMM) is employed to obtain both shock and oscillatory wave solutions from these equations, while parametric effects on wave characteristics are systematically examined. Chapter 3 investigates heavy ion-acoustic shock waves (HIASWs) in a plasma comprising inertial heavy ions, Maxwellian light ions, and (α,q)-distributed electrons, by deriving the Burgers, modified Burgers, and mixed modified Burgers equations. The study presents stationary shock wave solutions for these equations and examines how plasma parameters influence shock wave characteristics. Chapter 4 investigates the dust acoustic (DA) shock wave phenomena in an strongly coupled dusty plasma. By deriving Burgers equations with quadratic, cubic, and quartic nonlinearities, we analyze shock wave behavior near critical values (CVs) and super-critical values (SCVs), revealing how polarization force and coupling parameter modifies shock wave excitations. Chapter 5 analyzes heavy ion-acoustic (HIA) solitons and dressed solitons in weakly/strongly coupled plasmas with nonthermal electrons. Chapter 6 advances the Chapter 3 framework by examining HIASWs near CVs and SCVs, deriving a non-integrable NLEE with combined cubic-quartic nonlinearities that necessitates numerical solution via Runge-Kutta-Fehlberg analysis. Thus, the thesis enhances understanding of nonlinear coherent structures observed in various space and astrophysical environments.