Solitary, explosive, rational and elliptic doubly periodic solutions for nonlinear electron-acoustic waves in the earth's magnetotail region

TL;DR

This paper investigates various nonlinear electron acoustic wave solutions in Earth's magnetotail plasma, including solitary, elliptic, and explosive waves, using advanced analytical methods and numerical analysis.

Contribution

It introduces a novel algebraic method for obtaining exact solutions of the KdV equation in plasma physics, extending beyond traditional tanh methods.

Findings

Identification of bell-shaped solitary pulses and blowup solutions

Discovery of Jacobi and Weierstrass elliptic doubly periodic solutions

Observation of explosive pulse propagation in plasma environments

Abstract

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is used here. Numerical studies have been made using plasma parameters close to those values corresponding to Earth's plasma sheet boundary layer region reveals different solutions i.e., bell-shaped solitary pulses and singularity solutions at a finite point which called "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrass elliptic doubly periodic type solutions, in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as earth's magnetotail region and terrestrial magnetosphere.