Three dimensional ion acoustic solitary waves in a magnetized plasma consisting of two temperature nonextensive electrons

The study of ion-acoustic solitary waves in a magnetized plasma has long been considered to be an important research subject and plays an increasingly important role in scientific research. Previous studies have focused on the integer-order models of ion-acoustic solitary waves. With the development of theory and advancement of scientific research, fractional calculus has begun to be considered as a method for the study of physical systems. The study of fractional calculus has opened a new window for understanding the features of ion-acoustic solitary waves and can be a potentially valuable approach for investigations of magnetized plasma. In this paper, based on the basic system of equations for ion-acoustic solitary waves and using multi-scale analysis and the perturbation method, we have obtained a new model called the three-dimensional(3D) Schamel-KdV equation. Then, the integer-order 3D Schamel-KdV equation is transformed into the time-space fractional Schamel-KdV (TSF-Schamel-KdV) equation by using the semi-inverse method and the fractional variational principle. To study the properties of ion-acoustic solitary waves, we discuss the conservation laws of the new time-space fractional equation by applying Lie symmetry analysis and the Riemann-Liouville fractional derivative. Furthermore, the multi-soliton solutions of the 3D TSF-Schamel-KdV equation are derived using the Hirota bilinear method. Finally, with the help of the multi-soliton solutions, we explore the characteristics of motion of ion-acoustic solitary waves.

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The collisions of two ion acoustic solitary waves in a magnetized nonextensive plasma

Open Physics ◽

10.2478/s11534-014-0504-5 ◽

2014 ◽

Vol 12 (11) ◽

Cited By ~ 3

Author(s):

Emad El-Shamy ◽

Mouloud Tribeche ◽

Wael El-Taibany

Keyword(s):

Solitary Waves ◽

Negative Ions ◽

Phase Shifts ◽

Magnetized Plasma ◽

Nonextensive Electrons ◽

Oblique Collision ◽

Multicomponent Plasma ◽

Ion Acoustic Solitary Waves ◽

Ion Acoustic ◽

Analytical Phase

AbstractUsing the extended Poincaré-Lighthill-Kuo (EPLK) method, the interaction between two ion acoustic solitary waves (IASWs) in a multicomponent magnetized plasma (including Tsallis nonextensive electrons) has been theoretically investigated. The analytical phase shifts of the two solitary waves after interaction are estimated. The proposed model leads to rarefactive solitons only. The effects of colliding angle, ratio of number densities of (positive/negative) ions species to the density of nonextensive electrons, ion-to-electron temperature ratio, mass ratio of the negative-to-positive ions and the electron nonextensive parameter on the phase shifts are investigated numerically. The present results show that these parameters have strong effects on the phase shifts and trajectories of the two IASWs after collision. Evidently, this model is helpful for interpreting the propagation and the oblique collision of IASWs in magnetized multicomponent plasma experiments and space observations.

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Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons

Journal of Plasma Physics ◽

10.1017/s0022377809008113 ◽

2009 ◽

Vol 75 (5) ◽

pp. 593-607 ◽

Cited By ~ 1

Author(s):

SK. ANARUL ISLAM ◽

A. BANDYOPADHYAY ◽

K. P. DAS

Keyword(s):

Stability Analysis ◽

Solitary Wave ◽

Solitary Waves ◽

Perturbation Expansion ◽

Magnetized Plasma ◽

Wave Number ◽

First Order ◽

Zk Equation ◽

Ion Acoustic Solitary Waves ◽

Ion Acoustic

AbstractA theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.

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Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas

Nonlinear Processes in Geophysics ◽

10.5194/npg-11-219-2004 ◽

2004 ◽

Vol 11 (2) ◽

pp. 219-228 ◽

Cited By ~ 48

Author(s):

S. S. Ghosh ◽

G. S. Lakhina

Keyword(s):

Solitary Waves ◽

Nonlinear Theory ◽

Acoustic Waves ◽

Large Amplitude ◽

Magnetized Plasma ◽

Amplitude Variation ◽

Fully Nonlinear ◽

Weakly Nonlinear ◽

Ion Acoustic Solitary Waves ◽

Ion Acoustic

Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.

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