Comment on “Soliton solutions and chaotic motion of the extended Zakharov-Kuznetsov equations in a magnetized two-ion-temperature dusty plasma” [Phys. Plasmas 21, 073709 (2014)]

In the aforementioned paper we obtained an equation for non-linear Alfvén waves in a finite-β plasma, and investigated envelope soliton solutions thereof. The purpose of this note is to point out an error in the derivation of the soliton envelopes, and present corrected expressions for these solitons.The error arises from our assumption of translational invariance of both the envelope and phase of an envelope soliton expressed in equations (16) and (17). Rather, the phase is related to the amplitude by where y ≡ x — VEt is a comoving co-ordinate, and all other quantities are defined in the above paper.

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Non-planar dust-acoustic Gardner solitons with two-ion-temperature in a dusty plasma

Journal of Plasma Physics ◽

10.1017/s002237781100047x ◽

2011 ◽

Vol 78 (2) ◽

pp. 125-131 ◽

Cited By ~ 21

Author(s):

M. ASADUZZAMAN ◽

A. A. MAMUN

Keyword(s):

Dusty Plasma ◽

Reductive Perturbation Method ◽

Nonlinear Propagation ◽

Number Density ◽

Propagation Characteristics ◽

Ion Temperature ◽

Dust Acoustic ◽

Higher Temperature ◽

Basic Features ◽

Gardner Solitons

AbstractThe nonlinear propagation characteristics of Gardner solitons (GSs) in a non-planar (cylindrical and spherical) two-ion-temperature unmagnetized dusty plasma, whose constituents are inertial negative dust, Boltzmann electrons and ions with two distinctive temperatures, are investigated by deriving the modified Gardner (mG) equation. The standard reductive perturbation method is employed to derive the mG equation. The basic features of non-planar dust-acoustic (DA) GSs are analyzed. It has been found that the basic characteristics of GSs, which are shown to exist for the values of ni10/Zdnd0 around 0.311, for ni20/Zdnd0 = 0.5, Ti1/Te = 0.07, and Ti1/Ti2 = 0.05 [where ni10 (ni20) is the lower (higher) temperature ion number density at equilibrium, Ti1 (Ti2) is the lower (higher) temperature of ions, Te is the electron temperature, Zd is the number of electrons residing on the dust grain surface, and nd0 is the equilibrium dust number density] are different from those of Korteweg-de Vries solitons, which do not exist around ni10/Zdnd0 ≃ 0.311. It has been found that the propagation characteristics of non-planar DA GSs significantly differ from those of planar ones.

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Overtaking Collision and Phase Shifts of Dust Acoustic Multi-Solitons in a Four Component Dusty Plasma with Nonthermal Electrons

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0106 ◽

2015 ◽

Vol 70 (9) ◽

pp. 703-711 ◽

Cited By ~ 15

Author(s):

Gurudas Mandal ◽

Kaushik Roy ◽

Anindita Paul ◽

Asit Saha ◽

Prasanta Chatterjee

Keyword(s):

Dusty Plasma ◽

Kdv Equation ◽

Perturbation Technique ◽

Soliton Solutions ◽

Phase Shifts ◽

Nonlinear Propagation ◽

Bilinear Method ◽

Nonthermal Electrons ◽

Dust Acoustic ◽

Overtaking Collision

AbstractThe nonlinear propagation and interaction of dust acoustic multi-solitons in a four component dusty plasma consisting of negatively and positively charged cold dust fluids, non-thermal electrons, and ions were investigated. By employing reductive perturbation technique (RPT), we obtained Korteweged–de Vries (KdV) equation for our system. With the help of Hirota’s bilinear method, we derived two-soliton and three-soliton solutions of the KdV equation. Phase shifts of two solitons and three solitons after collision are discussed. It was observed that the parameters α, β, β1, μe, μi, and σ play a significant role in the formation of two-soliton and three-soliton solutions. The effect of the parameter β1 on the profiles of two soliton and three soliton is shown in detail.

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