The Kadomstev–Petviashvili equation in dusty plasma with variable dust charge and two temperature ions

Gill, Tarsem Singh; Saini, N. S.; Kaur, Harpreet

doi:10.1016/j.chaos.2005.08.118

Cited by 80 publications

(45 citation statements)

References 14 publications

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“…Notice that the derived parameter "a" is different from what has been reported in [11]. Our calculation shows that what has been appeared in [11] can not be correct.…”

Section: The Derivation Of Kp Equationcontrasting

confidence: 47%

“…The effect of dust temperature has been investigated in reference [6] and the normal modes of plasmas because of the existence of heavy dust particles have been modified in reference [7]. In most investigations reductive perturbation method has been used for deriving the 'kdv' or 'mkdv' equation in one-dimensional case [8][9][10] and also for KP equation in higher dimensions [11]. The charging process of dust particles is an important effect which has been investigated in [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Solitons of the KP equation in dusty plasma with variable dust charge and two temperature ions: energy and stability

Pakzad

Javidan

2009

Indian J Phys

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The propagation of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions is analyzed. By using the reductive perturbation theory, the Kadomtsev-Petviashivili (KP) equation is derived. A Sagdeev potential has been investigated. This potential is used to study the stability conditions for existence of solitonic solutions. Also, it is shown that a rarefactive soliton can exist in most of the cases. The energy of the soliton has been calculated and by using the standard normal-mode analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the amplitude, width and energy of soliton and its effects on the angular frequency of linear wave are also discussed.

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“…Notice that the derived parameter "a" is different from what has been reported in [11]. Our calculation shows that what has been appeared in [11] can not be correct.…”

Section: The Derivation Of Kp Equationcontrasting

confidence: 47%

Section: Introductionmentioning

confidence: 99%

Solitons of the KP equation in dusty plasma with variable dust charge and two temperature ions: energy and stability

Pakzad

Javidan

2009

Indian J Phys

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“…Gill et al [25] analyzed the properties of KP solitons in plasmas with two temperature ions and reported the formation of both the rarefactive and compressive solitons. In a similar study, Masood et al [26] reported the formation of two-dimensional nonplanar electrostatic shocks in an un-magnetized asymmetric pair-ion plasma and found that the kinematic viscosity enhances the shock strength.…”

Section: Introductionmentioning

confidence: 99%

Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Dev¹,

Sarma²,

Deka³

et al. 2014

Commun. Theor. Phys.

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Abstract:We study the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in an unmagnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili Burgers (KPB) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the KPB equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.PACS Numbers: 52.27.Lw, 52.35.Fp, 52.35.Tc IntroductionIn the last few decades, numerous investigations have been made on the study of nonlinear waves and structures in low-temperature dusty plasmas as the presence of extremely massive charged dust particles plays a vital role in understanding the electrostatic disturbances in space plasma environments [1][2][3] as well as laboratory plasma devices [4,5]. It has been pointed out that the static charged dust grains can drastically modify the existing response of electrostatic wave spectra in dusty plasmas [4][5][6][7][8][9][10][11]. On the other hand, depending upon whether the dust grains are static or mobile, there appear new types of electrostatic waves including solitary or shock waves in plasmas. Shukla and Silin first theoretically [12] investigated the existence of low-frequency dust-ion acoustic (DIA) waves (with phase speed much smaller than the electron thermal speed and larger than the ion thermal speed) in a three-component dusty plasma. Later, this DIA wave was experimentally observed by Barkan et al using a dusty plasma device [13].The Korteweg-de Vries (KdV) equation, which governs the evolution of solitary waves, was first derived by Washimi and Tanuiti in a normal two-component plasma [14] using a reductive perturbation technique. It has been reported that multi-component plasmas in presence of sufficient amount of negative ions can support both compressive and rarefactive KdV solitons [15]. Furthermore, the properties of DIA solitary waves and shocks as observed in laboratory dusty plasmas are well explained by the modified KdV and KdV-Burgers (KdVB) equations [5,11,16,17].

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“…Substituting equations (13)(14)(15)(16)(17) into equations (1-4) and collecting terms with same powers of , from the cofficients of lowest order we have:…”

Section: Mathematical Analysismentioning

confidence: 99%

“…We use the reductive perturbation technique to derive a KdV equation. would like to use the homogeneous balance method [15,16] to construct an auto-Bäcklund transformation (BT) [17][18][19][20][21][22][23] , new exact soliton solutions of KdV equation are obtained and we have applied the modifiedǴ G expansion method [24][25][26][27][28][29][30][31], the sine-cosine expansion method, the sinh-coshine expansion method ,and the sech-tanh expansion method [33,[37][38][39][40][41] and to obtain a new travelling wave solutions of KdV equation. The paper is organized as follows :This introduction in Section 1.…”

Section: Introductionmentioning

confidence: 99%

Auto-Backlund transformations and New Exact Soliton Solutions of KdV Equation for Nonlinear Dust Acoustic Solitary Waves in Dust Plasma with Variable Dust Charge

Ibrahim

2014

International Journal of Applied Mathematical Research

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The nonlinear properties of dust acoustic solitary waves in unmagnetized dust plasma consisting of negative charged dust particles , Boltzmann distributed electrons and non-thermal distributed ions with variable dust charge are investigated. By using the reductive perturbation theory, a Korteweg-de Veries (KdV) equation is derived. The Sagdeev's potential are obtained in terms of ion acoustic velocity by using the auto-Bäcklund (BT) transformation, the modifiedǴ G expansion, the sine-cosine expansion method, the sinh-coshine expansion method, and the sech-tanh expansion method describing the nonlinear propagation of ion-acoustic solitary waves in unmagnetized dust plasma.

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The Kadomstev–Petviashvili equation in dusty plasma with variable dust charge and two temperature ions

Cited by 80 publications

References 14 publications

Solitons of the KP equation in dusty plasma with variable dust charge and two temperature ions: energy and stability

Solitons of the KP equation in dusty plasma with variable dust charge and two temperature ions: energy and stability

Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Auto-Backlund transformations and New Exact Soliton Solutions of KdV Equation for Nonlinear Dust Acoustic Solitary Waves in Dust Plasma with Variable Dust Charge

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