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

2015 ◽  
Vol 70 (9) ◽  
pp. 703-711 ◽  
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.

Dust acoustic shock waves in arbitrarily charged dusty plasma with low and high temperature non-thermal ions

2015 ◽  
Vol 93 (10) ◽  
pp. 1030-1038 ◽  
Author(s):  
Apul N. Dev ◽  
Jnanjyoti Sarma ◽  
Manoj K. Deka
Keyword(s):  
Shock Waves ◽  
Dusty Plasma ◽  
Burgers Equation ◽  
Perturbation Technique ◽  
Nonlinear Propagation ◽  
Dust Particles ◽  
Charged Dust ◽  
Plasma Parameters ◽  
Tanh Method ◽  
Dust Acoustic

Using the well-known reductive perturbation technique, the three-dimensional (3D) Burgers equation and modified 3D Burgers equation have been derived for a plasma system comprising of non-thermal ions, Maxwellian electrons, and negatively charged fluctuating dust particles. The salient features of nonlinear propagation of shock waves in such plasmas have been investigated in detail. The different temperature non-thermal ions and Maxwellian electrons are found to play an important role in the shock waves solution. The analytical solution of the 3D Burgers equation and modified 3D Burgers equation ratifying the propagation of dust acoustic shock waves are derived using the well-known tanh method. On increasing the population of non-thermal ions, an enhancement in the amplitude of shock waves is seen for negatively charged dust particles. A striking dependence of amplitude and width of shock waves on the ratio of ion temperatures and densities are also reported. Finally we introduced a new stretching coordinate and perturbation for the nth-order nonlinear 3D Burgers equation and its solution by the use of the tanh method. We found that, due to higher nonlinearity, the amplitude of shock waves decreases while width remains constant for all plasma parameters considered in the present investigation. The features accounted here could be relevant in the case of different space and astrophysical plasmas and laboratory dusty plasma for negatively charged dust fluctuation.

scholarly journals Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Najah Kabalan ◽  
Mahmoud Ahmad ◽  
Ali Asad
Keyword(s):  
Theoretical Study ◽  
Kdv Equation ◽  
Perturbation Technique ◽  
Dusty Plasmas ◽  
Dust Grains ◽  
Bilinear Method ◽  
Laboratory Plasma ◽  
Strongly Coupled ◽  
Hirota Bilinear ◽  
Dusty Plasma System

The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton solution. It is found that coupling and structure parameters have a clear effect on the compressibility. These changes in the compressibility affected the amplitude and width of interactive solitons, in addition to the phase shifts resulting from the interaction. These results can be used to understand the behavior of solitary waves that occur in various natural and laboratory plasma environments with dust impurity situations.

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

2011 ◽  
Vol 78 (2) ◽  
pp. 125-131 ◽  
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.

Arbitrary amplitude dust-acoustic solitons in a weakly non-ideal plasma with non-thermal ions

2007 ◽  
Vol 73 (5) ◽  
pp. 671-686 ◽  
Author(s):  
S. K. MAHARAJ ◽  
R. BHARUTHRAM ◽  
S. R. PILLAY
Keyword(s):  
Soliton Solutions ◽  
Thermal Parameter ◽  
Nonlinear Propagation ◽  
Charged Dust ◽  
Dust Acoustic Wave ◽  
Dust Acoustic ◽  
Arbitrary Amplitude ◽  
Dust Fluid ◽  
Lower Limits ◽  
Ideal Plasma

AbstractThe nonlinear propagation of the dust-acoustic wave is investigated in a weakly non-ideal plasma comprising Boltzmann electrons, non-thermal ions characterized by a non-thermal parameter α and a negatively charged dust fluid. The non-ideal dust fluid is represented by the van der Waals equation of state. Arbitrary amplitude soliton solutions are found to occur for both supersonic and subsonic values of the Mach number. Upper and lower limits of the range of values of α for which solitons exist are examined as a function of the non-ideal parameters associated with the effects of volume reduction and the cohesive forces, for both the supersonic and subsonic cases.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

scholarly journals Interaction of Dust-Acoustic Shock Waves in a Magnetized Dusty Plasma under the Influence of Polarization Force

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
N. S. Saini ◽  
Kuldeep Singh ◽  
Papihra Sethi
Keyword(s):  
Shock Waves ◽  
Dusty Plasma ◽  
Phase Shifts ◽  
Physical Parameters ◽  
Charged Dust ◽  
Nonlinear Structures ◽  
Plk Method ◽  
Polarization Force ◽  
Magnetized Dusty Plasma ◽  
Dust Acoustic

The interaction of dust-acoustic (DA) shock waves in a magnetized dusty plasma under the influence of nonextensively modified polarization force is investigated. The plasma model consists of negatively charged dust, Maxwellian electrons, nonextensive ions, and polarization force. In this investigation, we have derived the expression of polarization force in the presence of nonextensive ions and illustrated the head-on collision between two DA shock waves. The extended Poincaré–Lighthill–Kuo (PLK) method is employed to obtain the two-sided Korteweg–de Vries–Burgers (KdVB) equations and phase shifts of two shock waves. The trajectories and phase shifts of negative potential dust-acoustic shock waves after collision are examined. The combined effects of various physical parameters such as polarization force, nonextensivity of ions, viscosity of dust, and magnetic field strength on the phase shifts of DA shock waves have been studied. The present investigation might be useful to study the process of collision of nonlinear structures in space dusty plasma such as planetary rings where non-Maxwellian particles such as nonextensive ions, negatively charged dust, and electrons are present.

Three-Soliton Interaction and Soliton Turbulence in Superthermal Dusty Plasmas

2019 ◽  
Vol 74 (9) ◽  
pp. 757-766 ◽  
Author(s):  
Rustam Ali ◽  
Prasanta Chatterjee
Keyword(s):  
Wave Field ◽  
Kdv Equation ◽  
Perturbation Technique ◽  
Great Influence ◽  
Dusty Plasmas ◽  
Second Order ◽  
Soliton Interaction ◽  
Bilinear Method ◽  
The Kdv Equation ◽  
Skewness And Kurtosis

AbstractPropagation and interaction of three solitons are studied within the framework of the Korteweg-de Vries (KdV) equation. The KdV equation is derived from an unmagnetised, collision-less dusty plasma containing cold inertial ions, stationary dusts with negative charge, and non-inertial kappa-distributed electrons, using the reductive perturbation technique (RPT). Adopting Hirota’s bilinear method, the three-soliton solution of the KdV equation is obtained and, as an elementary act of soliton turbulence, a study on the soliton interaction is presented. The concavity of the resulting pulse is studied at the strongest interaction point of three solitons. At the time of soliton interaction, the first- and second-order moments as well as the skewness and kurtosis of the wave field are calculated. The skewness and kurtosis decrease as a result of soliton interaction, whereas the first- and second-order moments remain invariant. Also, it is observed that the spectral index κ and the unperturbed dust-to-ion ratio μ have great influence on the skewness and kurtosis of the wave field.

Adiabatic dust-acoustic waves with dust-charge fluctuations

1998 ◽  
Vol 60 (3) ◽  
pp. 541-550 ◽  
Author(s):  
S. V. SINGH ◽  
N. N. RAO
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Plasma Pressure ◽  
Charge Fluctuations ◽  
Dust Acoustic Waves ◽  
Dust Charge ◽  
Dust Acoustic ◽  
Supersonic Regime ◽  
Dust Charge Fluctuations

We study the effect of charge fluctuations on the propagation of adiabatic linear and nonlinear dust-acoustic waves by considering the electrons and ions to be in Boltzmann equilibria, and the dust grains to satisfy the fluid equations with full adiabatic equation of state. Linear dust-acoustic waves are damped owing to the dust-charge fluctuations, and the damping rate decreases with increasing adiabatic dust pressure. Nonlinear dust-acoustic waves are governed by the set of coupled Boussinesq-like and dust-charge perturbation equations. It is shown that for unidirectional propagation, the Boussinesq-like equation reduces to usual Korteweg–de Vries (KdV) equation. At early times, the localized solutions of the KdV equation are damped owing to the dust-charge perturbations. The soliton amplitude decreases with increasing adiabatic dust plasma pressure and increases with Mach number. Soliton solutions are found only in the supersonic regime.

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