Analytical Solitary Wave Solution of the Dust Ion Acoustic Waves for the Damped Forced Korteweg–de Vries Equation in Superthermal Plasmas

2018 ◽  
Vol 73 (2) ◽  
pp. 151-159 ◽  
Author(s):  
Prasanta Chatterjee ◽  
Rustam Ali ◽  
Asit Saha
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Dusty Plasmas ◽  
Periodic Force ◽  
Ion Acoustic ◽  
De Vries ◽  
Dia Waves

AbstractAnalytical solitary wave solution of the dust ion acoustic (DIA) waves was studied in the framework of the damped forced Korteweg–de Vries (DFKdV) equation in superthermal collisional dusty plasmas. The reductive perturbation technique was applied to derive the DKdV equation. It is observed that both the rarefactive and compressive solitary wave solutions are possible for this plasma model. The effects of κ and the strength (f0) and frequency (ω) of the external periodic force were studied on the analytical solitary wave solution of the DIA waves. It is observed that the parameters κ, f0 and ω have significant effects on the structure of the damped forced DIA solitary waves. The results of this study may have relevance in laboratory plasmas as well as in space plasmas.

Effect of Dust Ion Collision on Dust Ion Acoustic Solitary Waves for Nonextensive Plasmas in the Framework of Damped Korteweg–de Vries–Burgers Equation

2019 ◽  
Vol 74 (10) ◽  
pp. 861-867 ◽  
Author(s):  
Niranjan Paul ◽  
Kajal Kumar Mondal ◽  
Prasanta Chatterjee
Keyword(s):  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Viscosity Coefficient ◽  
Travelling Wave ◽  
Physical Parameters ◽  
Charged Dust ◽  
Ion Acoustic ◽  
De Vries ◽  
Ion Collision

AbstractAnalytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the framework of the damped Korteweg–de Vries–Burgers (DKdVB) equation in an unmagnetised collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, q-nonextensive electrons, and neutral particles. Using Reductive Perturbation Technique, the DKdVB equation is obtained for DIAWs. The effects of different physical parameters such as dust ion collision frequency parameter (\({\nu_{id0}}\)), viscosity coefficient (η10), the entropic index (q), the speed of the travelling wave (M0), and the ratio between the unperturbed densities of the electrons and ions (μ) on the analytical solution of DIAWs are observed. The results of the present article may have applications in laboratory and space plasmas.

scholarly journals Approximate Analytical Solution of Nonlinear Evolution Equations

2020 ◽  
Author(s):  
Laxmikanta Mandi ◽  
Kaushik Roy ◽  
Prasanta Chatterjee
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Nonlinear Evolution Equations ◽  
Charged Dust ◽  
De Vries ◽  
Frame Work ◽  
Dust Grain ◽  
Charged Ions

Analytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the frame-work of Korteweg-de Vries (KdV), damped force Korteweg-de Vries (DFKdV), damped force modified Korteweg-de Vries (DFMKdV) and damped forced Zakharov-Kuznetsov (DFZK) equations in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, Maxwellian distributed electrons and neutral particles. Using reductive perturbation technique (RPT), the evolution equations are obtained for DIAWs.

Alternative ion-acoustic solitary waves in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability

2007 ◽  
Vol 73 (6) ◽  
pp. 869-899 ◽  
Author(s):  
JAYASREE DAS ◽  
ANUP BANDYOPADHYAY ◽  
K.P. DAS
Keyword(s):  
Distribution Function ◽  
Solitary Wave ◽  
Velocity Distribution ◽  
Solitary Waves ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Velocity Distribution Function ◽  
Trapped Electrons ◽  
Zk Equation ◽  
Ion Acoustic

AbstractThe solitary structures of the ion-acoustic waves have been considered in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having a vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is governed by the Schamel's modified Korteweg–de Vries–Zakharov–Kuznetsov (S-ZK) equation. This equation admits solitary wave solutions having a profile sech4. When the coefficient of the nonlinear term of this equation vanishes, the vortex-like velocity distribution function of electrons simply becomes the non-thermal velocity distribution function of electrons and the nonlinear behaviour of the same ion-acoustic wave is described by a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. This equation admits solitary wave solutions having a profile sech2. A combined S–KdV–ZK equation more efficiently describes the nonlinear behaviour of an ion-acoustic wave when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons, i.e. when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having a profile different from either sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been derived. It is found that this alternative solitary wave solution approaches the solitary wave solution (the sech2 profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero. The three-dimensional stability of these solitary waves propagating obliquely to the external uniform and static magnetic field has been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of the instability have been derived at the lowest order. It is also found that the instability condition and growth rate of instability of the alternative solitary waves are exactly the same as those of the solitary waves as determined from the KdV-ZK equation (the sech2 profile) when the contribution of trapped electrons tends to zero.

scholarly journals Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150416 ◽  
Author(s):  
Roger Grimshaw ◽  
Yury Stepanyants ◽  
Azwani Alias
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Anomalous Dispersion ◽  
Essential Difference ◽  
De Vries ◽  
Long Time ◽  
Ostrovsky Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

It is well known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg–de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here, we examine the same initial condition for the Ostrovsky equation with anomalous dispersion, when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrödinger equation, based at that wavenumber where the phase and group velocities coincide. Long-time numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg–de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg–de Vries solitary wave.

Obliquely propagating dust–ion acoustic solitary waves and their multidimensional instabilities in magnetized dusty plasmas with bi-maxwellian electrons

2013 ◽  
Vol 91 (7) ◽  
pp. 530-536 ◽  
Author(s):  
M.M. Masud ◽  
N.R. Kundu ◽  
A.A. Mamun
Keyword(s):  
Solitary Waves ◽  
Perturbation Technique ◽  
Dusty Plasmas ◽  
Nonlinear Propagation ◽  
Instability Criterion ◽  
Magnetized Dusty Plasma ◽  
Perturbation Mode ◽  
Ion Acoustic ◽  
Higher Temperature ◽  
Dia Waves

The nonlinear propagation of dust–ion acoustic (DIA) waves in an obliquely propagating magnetized dusty plasma, consisting of bi-maxwellian electrons (namely lower and higher temperature maxwellian electrons), negatively charged immobile dust grains, and inertial ions is rigorously investigated by deriving the Zakharov–Kuznetsov equation. Later, the multidimensional instability of the DIA solitary waves (DIASWs) is analyzed using the small-k perturbation technique. It is investigated that the nature of the DIASWs, the instability criterion, and the growth rate of the perturbation mode are significantly modified by the external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes. The implications of the results obtained from this investigation in space and laboratory dusty plasmas are briefly discussed.

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