Obliquely propagating cnoidal waves in a magnetized dusty plasma with variable dust charge

Yadav, Lakhan Lal; Sayal, V.K.

doi:10.1063/1.3255593

Cited by 21 publications

(6 citation statements)

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“…Dust acoustic non linear periodic waves in dusty plasma with charge fluctuations have been theoretically studied by Yadav et al 22 and found that the frequency of cnoidal waves is function of amplitude and its phase velocity was found to decrease (increase) below (above) the critical value of modulus k 2 ¼ 0.949. Investigations of obliquely propagating cnoidal waves in a magnetized dusty plasma with variable dust charge made by Yadav et al 23 indicates that contribution to dispersion due to deviation from plasma approximation is dominant for small angle of obliqueness, whereas dispersion due to magnetic field becomes dominant for large angle of obliqueness and frequency of cnoidal wave was found to depend on the wave amplitude. The study of ion acoustic non-linear periodic waves in electron-positron ion plasma using reductive perturbation method was made by Chawla and Mishra 24 and found that the positron concentration modifies the characteristics of cnoidal waves and its amplitude increases with increase in positron concentration.…”

Section: Introductionmentioning

confidence: 97%

Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma

2012

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Using reductive perturbation method with appropriate boundary conditions, coupled evolution equations for first and second order potentials are derived for ion-acoustic waves in a collisionless, un-magnetized plasma consisting of hot isothermal electrons, cold ions, and massive mobile charged dust grains. The boundary conditions give rise to renormalization term, which enable us to eliminate secular contribution in higher order terms. Determining the non secular solution of these coupled equations, expressions for wave phase velocity and averaged non-linear ion flux associated with ion-acoustic cnoidal wave are obtained. Variation of the wave phase velocity and averaged non-linear ion flux as a function of modulus (k2) dependent wave amplitude are numerically examined for different values of dust concentration, charge on dust grains, and mass ratio of dust grains with plasma ions. It is found that for a given amplitude, the presence of positively (negatively) charged dust grains in plasma decreases (increases) the wave phase velocity. This behavior is more pronounced with increase in dust concentrations or increase in charge on dust grains or decrease in mass ratio of dust grains. The averaged non-linear ion flux associated with wave is positive (negative) for negatively (positively) charged dust grains in the plasma and increases (decreases) with modulus (k2) dependent wave amplitude. For given amplitude, it increases (decreases) as dust concentration or charge of negatively (positively) charged dust grains increases in the plasma.

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Section: Introductionmentioning

confidence: 97%

Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma

2012

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“…In physical space, the electric potential increases from zero (at ζ = −∞), attains a maximum value at = 0, and then decreases until it becomes zero (at ζ = ∞). This potential structure does not repeat and it represents an ion-acoustic soliton [26]. with the numerical values of Rahman et al [11].…”

Section: Numerical Results and Discussionmentioning

confidence: 92%

“…In order to investigate the propagation of nonlinear periodic ion-acoustic and solitary waves in a dense relativistic degenerate magnetoplasma, we follow the reductive perturbation technique, which leads to a scaling of the independent variables through the stretched coordinates [26],…”

Section: Derivation Of the Nonlinear Modified Kdv Equationmentioning

confidence: 99%

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma

2015

Phys. Rev. E

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The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

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“…Similarly, due to the Equations (9) and (10) in the present study, we consider Δ ∝ ε −1/2 and (V − 1) ∝ ε, where V is the normalized phase velocity of the OIIASs, which gives the velocity of the non-linear wave along the ξ direction, and ε is a real small parameter (0< ε <1), which measures the strength of non-linearity and the weakness of the dispersion. Therefore, to obtain the non-linear wave, which is considered to be a one-dimensional simple wave stationary in the moving frame ξ, we utilize the stretched coordinates as [6,30,41,[43][44][45][46][47]…”

Section: Non-linear Analysismentioning

confidence: 99%

“…Similarly, due to the Equations (9) and (10) in the present study, we consider ∆ ∝ ϵ −1/2 and (V − 1) ∝ ϵ, where V is the normalized phase velocity of the OIIASs, which gives the velocity of the non‐linear wave along the ξ direction, and ϵ is a real small parameter (0< ϵ <1), which measures the strength of non‐linearity and the weakness of the dispersion. Therefore, to obtain the non‐linear wave, which is considered to be a one‐dimensional simple wave stationary in the moving frame ξ, we utilize the stretched coordinates as [ 6,30,41,43–47 ]

ξ = ϵ^{1 / 2} false(ℓ_{normalx} X + ℓ_{normaly} Y + ℓ_{normalz} Z - VT false),

τ = {normalε}^{3 / 2} T,

where ℓ x , ℓ y , and ℓ z are the directional cosines of the wave vector

\overset{true\to}{normalk}

along the X, Y, and Z axes, respectively, so that

ℓ_{x}^{2} + ℓ_{y}^{2} + ℓ_{z}^{2} = 1 .

Using Equations (11a) and (11b), the exact stationary solution can be found for OIIASs propagating obliquely to a magnetic field. The expansions of the physically dependent variables to their equilibrium values are given by [ 6,43 ] :

Ψ = {normalΨ}^{(0)} + \sum_{n = 1}^{normal∞} {normalε}^{(n)} {normalΨ}^{(n)},

…”

Section: Non‐linear Analysismentioning

confidence: 99%

Overtaking collisions of oblique isothermal ion‐acoustic multisolitons in ultra‐relativistic degenerate dense magnetoplasmas

El-Shamy

Selim

El-Depsy

et al. 2020

Contributions to Plasma Physics

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Overtaking collisions of oblique isothermal ion-acoustic multisolitons are studied in an ultra-relativistic degenerate dense magnetoplasma, containing non-degenerate inertial warm ions and ultra-relativistic degenerate inertialess electrons and positrons. A non-linear Korteweg-de Vries (KdV) equation describing oblique isothermal ion-acoustic solitons (OIIASs) in such a plasma model is derived. By applying Hirota's bilinear method (HBM), the overtaking collisions of oblique isothermal ion-acoustic multisoliton solutions are investigated. An in-depth discussion shows that the amplitude, the width, and the phase shift of isothermal ion-acoustic multisolitons increase as the obliqueness and the chemical potential of electrons increase. The deviation of the trajectories decreases with increasing concentration of fermions and the ion cyclotron frequency. The present finding of this study is applicable in compact objects, such as white dwarfs and neutron stars, having degenerate ultra-relativistic dense electrons and positrons.

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Obliquely propagating cnoidal waves in a magnetized dusty plasma with variable dust charge

Cited by 21 publications

References 34 publications

Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma

Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma

Overtaking collisions of oblique isothermal ion‐acoustic multisolitons in ultra‐relativistic degenerate dense magnetoplasmas

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