Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers

Wedad Albalawi,Waqas Masood,Rabia Jahangir,Samir A El-Tantawy,Sadah A Alkhateeb

doi:10.3390/sym13112029

Abstract

The propagation of electron-acoustic waves (EAWs) in an unmagnetized plasma, comprising (r,q)-distributed hot electrons, cold inertial electrons, and stationary positive ions, is investigated. Both the unmodulated and modulated EAWs, such as solitary waves, rogue waves (RWs), and breathers are discussed. The Sagdeev potential approach is employed to determine the existence domain of electron acoustic solitary structures and study the perfectly symmetric planar nonlinear unmodulated structures. Moreover, the nonlinear Schrödinger equation (NLSE) is derived and its modulated solutions, including first order RWs (Peregrine soliton), higher-order RWs (super RWs), and breathers (Akhmediev breathers and Kuznetsov–Ma soliton) are presented. The effects of plasma parameters and, in particular, the effects of spectral indices r and q, of distribution functions on the characteristics of both unmodulated and modulated EAWs, are examined in detail. In a limited cases, the (r,q) distribution is compared with Maxwellian and kappa distributions. The present investigation may be beneficial to comprehend and predict the modulated and unmodulated electron acoustic structures in laboratory and space plasmas.

Highlights

Introduction published maps and institutional affilThe electron-acoustic waves (EAWs), first proposed by Fried and Gould in 1961 [1], have been extensively investigated in laboratory experiments [2] and observed in various areas of Earth’s magnetosphere, such as geomagnetic tails [3], bow shock [4], Earth’s magnetosheath [5], polar cusp [6], and dayside auroral region [7]
The Sagdeev potential approach is devoted to the study of unmodulated arbitrary amplitude electron acoustic solitary waves (EASWs)
The propagation of electrostatic electron-acousticmodulated waves in a nonMaxwellian plasma consisting of two-temperature electrons (hot electrons following (r, q) distribution and cold inertial electrons) and stationary positive ions were investigated

Summary

Physical Model and Governing Equations

Consider a collisionless unmagnetized plasma consisting of (r, q) distributed hot electrons (with density nh ), cold inertial electrons (with density nc ), and stationary positive ion (with density ni ). The condition of charge neutrality reads ni0 = ne0 = nc0 + nh0 , where nh0 , nc0 and ni0 represent the unperturbed number densities of hot electrons, cold electrons, and positive ions, respectively. The normalized number density of generalized (r, q)-distributed hot electrons is given by [28]. R and q are sometimes called the flatness and tail parameters This is the general distribution, in the sense that Maxwellian distribution is retrieved for r = 0 and q → ∞ and kappa distribution is recovered for r = 0 and q → κ + 1. For physically meaningful results, the following conditions must be fulfilled: q > 1 and q(r + 1) > 5/2 [28]

Sagdeev Potential Approach

Unmodulated Electron-Acoustic Solitary Waves

Nonlinear Schrödinger Equation and Modulational Instability

Electron Acoustic RWs and Breathers

Conclusions

Results