Periodic and localized structures in dusty plasma with Kaniadakis distribution

Khalid, Muhammad; Khan, Muhammad Bilal; Muddusir,; Ata-ur-Rahman, Ata-ur-Rahman; Irshad, Muhammad

doi:10.1515/zna-2021-0164

Cited by 18 publications

(7 citation statements)

References 48 publications

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“…Diverse approaches have been attained to study such models aiming to construct their wave solutions and discuss their behavior and properties. The most popular approaches are: the improved auxiliary differential equation method [4], the extended direct algebraic method [5,6], Lie point symmetries, reductions, conservation laws [7][8][9], the solitary wave ansatze [10], the reductive perturbation method [11][12][13], the homogeneous balance method [14], the direct symmetry method [15], the extended ( ) ¢ -G G 2 expansion method [16,17], the sine-Gordon expansion method and the ( ) ¢ -G 1…”

Section: Introductionmentioning

confidence: 99%

Qualitative analysis and new exact solutions for the extended space-fractional stochastic (3 + 1)-dimensional Zakharov-Kuznetsov equation

Elbrolosy

2024

Phys. Scr.

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In this paper, the extended (3 + 1)-dimensional Zakharov-Kuznetsov equation, which describes the propagation of ion-acoustic waves in a magnetic environment, is investigated. Due to the exposure of the propagation to unpredictable factors, the stochastic model is assessed including the Brownian process, in addition to including the recent concept of truncated M-fractional derivative. A fractional stochastic transformation is applied to transform the model into an integer-order ordinary differential equation which in turn is equivalent to a conservative Hamiltonian model. Novel solutions, such as hyperbolic, trigonometric, and Jacobian elliptic functions, are established by employing both of the qualitative analysis of dynamical systems and the first integral of the Hamiltonian model. We explore and graphically display the effects of the fractional derivative order and noise intensity on the solutions structures. In the deterministic instance, i.e., in the absence of noise, solitary and cnoidal solutions among other traveling wave solutions of the Zakharov-Kuznetsov equation, are derived. Further, it is found that the curvature of the wave disturbs and the surface turns substantially flat by increasing the value of noise. While the curve in all cases loses its characteristic shape and degenerates into another deterministic shape by changing the fractional derivative order.

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Section: Introductionmentioning

confidence: 99%

Qualitative analysis and new exact solutions for the extended space-fractional stochastic (3 + 1)-dimensional Zakharov-Kuznetsov equation

Elbrolosy

2024

Phys. Scr.

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“…The Kaniadakis distribution has been used to investigate the influence of the parameter 𝜅 on various plasma electrostatic waves, such as nonlinear IAWs, DIASWs, as well as electron-acoustic waves (EAWs). [20][21][22][23][24] Additionally, the Kaniadakis distribution has been applied to study Jeans instabilities in self-gravitating matter systems, quark-gluon plasma formation, and black-body radiation. [25][26][27] Its applications also extend to quantum systems, where it has been used to study the kinetics of photons and interacting atoms.…”

Section: Introductionmentioning

confidence: 99%

The role of κ‐deformed Kaniadakis distributed electrons on the dust ion‐acoustic waves in charge‐varying dusty plasma

Bellahsene,

Bacha,

Zerguini

2023

Contrib. Plasma Phys

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The one‐dimensional dynamics of nonlinear electrostatic dust‐ion acoustic waves (DIAWs), in a plasma containing Kaniadakis‐distributed electrons, fluid ions, and variable‐charge dust grains has been investigated. The κ−generalized electron charging current is derived based on the orbit‐motion limited approach. The reductive perturbation technique has been used to derive a KdV Burger equation of propagation. We have highlighted the dependence between the values of the dust particles charge Qd0 and the validity domain of the Kaniadakis parameter κ, where the Burger term C has positive. By integrating the KdV Burger equation numerically and assuming a laboratory dusty plasma, a transition from oscillatory to monotonic shock waves is observed with increasing values of κ. We have also found that the phase velocity of DIA shock waves decreases, and the dissipation can prevail over that of dispersion as the electrons move further away from thermal equilibrium (κ is increased). The coexistence of compressive and rarefactive of monotonic shock profile is observed. It is found that an increase in κ leads to an increase of the compressive monotonic shock wave and decrease the rarefactive monotonic shock wave.

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“…The investigation of nonlinear waves [24][25][26][27][28][29][30][31][32][33] in plasma and other dispersive media has received a great deal of attention due to their applications in different areas of physics including the nonlinear ion transport phenomena. In 1895, Korteweg and de Vries (KdV) derived the KdV equation, which is used to describe the dynamics of SWs [34,35].…”

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confidence: 99%

Oblique propagation of ion-acoustic solitary waves in magnetized electron-positron-ion plasma with Cairns distribution

Khalid¹,

Ullah²,

Kabir³

et al. 2022

EPL

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The propagation of ion acoustic (IA) solitary waves (SWs) is investigated in a magnetized electron–positron-ion (EPI) plasma with Cairns distributed electrons and positrons. The Korteweg-de Vries (KdV) and modified KdV (mKdV) equations are derived for the potential by employing the reductive perturbation technique (RPT) and its solitary wave (SW) solutions are analyzed. The effect of relevant plasma parameters (viz., nonthermality parameter β, positron concentration γ, ion thermality δ and magnetic field strength ) on the characteristics of IA solitary structures are discussed in detail.

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Periodic and localized structures in dusty plasma with Kaniadakis distribution

Cited by 18 publications

References 48 publications

Qualitative analysis and new exact solutions for the extended space-fractional stochastic (3 + 1)-dimensional Zakharov-Kuznetsov equation

Qualitative analysis and new exact solutions for the extended space-fractional stochastic (3 + 1)-dimensional Zakharov-Kuznetsov equation

The role of κ‐deformed Kaniadakis distributed electrons on the dust ion‐acoustic waves in charge‐varying dusty plasma

Oblique propagation of ion-acoustic solitary waves in magnetized electron-positron-ion plasma with Cairns distribution

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