Nonlinear Evolutionary Stages of a Dispersive Kappa Distributed Magnetized Plasma

We have examined a magnetized plasma, where the electron distribution follows a kappa distribution. Our focus is on studying the propagation of ion acoustic modes. Employing the reductive perturbation method, we derived an evolutionary equation, revealing a 3-D Zakharov-Kuznetsov (ZK) equation. Utilizing the Runge-Kutta (RK4) technique, we numerically solved the equation, varying parameters for comprehensive analysis. Subsequently, we conducted a phase plane analysis by transforming our evolutionary equation into a pair of ordinary differential equations (ODEs). Through this dynamical system analysis, we extracted substantial data concerning the stability of stationary structures represented by the ZK equation.