Sagdeev’s approach to study the effect of the kinematic viscosity on the dust ion-acoustic solitary waves in dusty plasma

Maitra, Subhamoy; Roychoudhury, Rajkumar

doi:10.1063/1.1885479

Cited by 13 publications

(8 citation statements)

References 32 publications

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“…With the knowledge of the above coefficients, one can write down the explicit solution of the mKdV-Burgers equation (21) in terms of tanh function Another type of solution can be obtained when the dissipation term is dominant over the dispersion term. In this case, Eq.…”

Section: Shock Wave Solutionsmentioning

confidence: 99%

“…So, in the dissipative case, it is reasonable to deal with dH dv rather than H. The mKdV-Burgers Eq. (21) can be written in the general form as…”

Section: Nonlinear Analysis Derivation Of the Mkdv-burgers Equationmentioning

confidence: 99%

“…Among such theoretical studies on dusty plasma, many authors studied solitary and shock waves in the frame of KdV-Burgers, mKdV-Burgers, KP-Burgers and mKPBurgers-type equations, which are usually deduced from a dissipative plasma system. The dust fluid dissipation could be caused by dust fluid viscosity, dust-dust collision, dust charge fluctuation, and Landau damping, which would modify the wave structures [15,21,28,47], and shock waves can be excited in the system under appropriate conditions. Shukla and Mamun [38] derived KdV-Burgers equation by reductive perturbation method and they have analysed the properties of nonlinear waves (solitons and shock waves) for strongly coupled unmagnetized dusty plasmas.…”

Section: Introductionmentioning

confidence: 99%

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Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

et al. 2015

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The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number k, the dust kinematic viscosity coefficient g d and the ratio of the ions to the electrons temperatures r i is discussed. In the nonlinear analysis, the modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV-Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.

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Section: Shock Wave Solutionsmentioning

confidence: 99%

“…So, in the dissipative case, it is reasonable to deal with dH dv rather than H. The mKdV-Burgers Eq. (21) can be written in the general form as…”

Section: Nonlinear Analysis Derivation Of the Mkdv-burgers Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

et al. 2015

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“…[3][4][5] The DIA wave was the extension of the usual ion acoustic waves, where the inertia is provided by the ions and the restoring force comes from the inertialess Boltzmann distributed electrons. After the pioneer work of the Shukla, the linear and nonlinear properties of the DIA waves were fully investigated in the unmagnetized [6][7][8] or magnetized 9-11 dusty plasmas. The linear theory was only valid when the amplitude of DIA was small, while the nonlinearity was not always neglected as the amplitude of the DIA waves were sufficiently large.…”

Section: The Effects Of Nonadiabatic Dust Charge Variation and Ultravmentioning

confidence: 99%

The effects of nonadiabatic dust charge variation and ultraviolet irradiation on the modulational instability of dust ion acoustic waves

et al. 2010

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The effects of nonadiabatic dust charge fluctuation on the nonlinear propagation of the dust ion acoustic (DIA) waves in the dusty plasma with positively charged dust grains have been investigated. By using the reductive perturbation technique, a three-dimensional modified nonlinear Schrödinger equation (mNLSE) governing the nonlinear envelope DIA waves was derived and the approximate solitary wave solution of the mNLSE was also obtained in the weak effect of nonadiabatic dust charge fluctuation limit, which shows that the amplitude of the DIA solitary wave exponentially decreases with time due to the collisionless dissipation caused by the nonadiabatic dust charge variation. The frequency, instability growth rate, and the critical modulational wave number of the small amplitude modulation are all dependent on photoelectron generated by ultraviolet irradiation and time due to the presence of nonadiabatic dust charge variation. The transverse perturbation plays an important role in the modulational instability region.

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“…Maitra et al 27 studied the effect of the kinematic viscosity on the DIA solitary waves in a dusty plasma. They used Sagdeev's technique and obtained exact analytical results for small amplitude DIA solitary waves.…”

Section: Introductionmentioning

confidence: 99%

Higher-order contribution to dust-ion acoustic dressed solitons in a warm dusty plasma

El-Bedwehy

2008

Physics of Plasmas

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Propagations of ion-acoustic dressed solitons in an unmagnetized dusty plasma consisting of a mixture of hot nonisothermal electrons, warm ions, and high negatively charged warm dust particles have been investigated. The reductive perturbation theory has been employed. At the lowest order of the perturbation theory a modified Korteweg–de Vries equation is obtained. At the next order of the perturbation theory, a linear inhomogeneous equation is obtained. Using the renormalization procedure introduced by Kodama and Taniuti, a stationary solution of the coupled equations has been obtained.

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Sagdeev’s approach to study the effect of the kinematic viscosity on the dust ion-acoustic solitary waves in dusty plasma

Cited by 13 publications

References 32 publications

Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

The effects of nonadiabatic dust charge variation and ultraviolet irradiation on the modulational instability of dust ion acoustic waves

Higher-order contribution to dust-ion acoustic dressed solitons in a warm dusty plasma

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