Phase plane analysis of small amplitude electron-acoustic supernonlinear and nonlinear waves in magnetized plasmas

Abstract

Phase plane analysis of small amplitude electron-acoustic supernonlinear and nonlinear waves in a magnetized nonextensive electron-ion plasma is examined. These electron-acoustic waves (EAWs) are studied based on the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. The dynamical systems for both the KdV and mKdV equations are formed using the propagating wave transfiguration. Phase plane analyses of EAWs corresponding to the KdV and mKdV equations are shown. Analytical solution corresponding to the electron-acoustic solitary wave for the KdV equation is derived. Analytical forms of kink, anti-kink and periodic wave solutions in ranges −1 < q < 0 and 0 < q < 1 are obtained for the mKdV equation. Superperiodic EAWs under the mKdV equation in the range q > 1 are shown numerically. Existence of small amplitude superperiodic EAWs under the mKdV equation is shown for the first time in a magnetized nonextensive electron-ion plasma using the concept of planar dynamical systems. Effects of system parameters on different traveling wave solutions of EAWs are displayed. Outcome of the study can be implemented to understand nonlinear and supernonlinear EAWs in space and atmosphere, such as, auroral zones and magnetosphere.