Solitary, explosive, and periodic solutions of the quantum Zakharov-Kuznetsov equation and its transverse instability

Moslem, W. M.; Ali, S.; Shukła, P. K.; Tang, Xuehan; Rowlands, G.

doi:10.1063/1.2757612

Cited by 115 publications

(67 citation statements)

References 49 publications

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“…In [14], some types of periodic wave solution and solitary wave solutions of the QZK equation have been obtained by extended Conte's truncation method [19] and the bending instability of the solitons are also investigated by small-k perturbation expansion method [20,21]. The aim of this paper is to use auxiliary equation method and Hirota bilinear method to investigate the QZK equation.…”

Section: Introductionmentioning

confidence: 99%

“…Khan and Masood [9] have rediscovered ZK equation [13], which was presented three decades ago and has been used to study the ion-acoustic waves in magnetized plasmas. Very recently, Moslem et al [14] have derived the quantum Zakharov-Kuznetsov (QZK) equation for electron-ion quantum plasmas and solitary explosive and periodic solutions are presented. The authors have also discussed the stability of the wave.…”

Section: Introductionmentioning

confidence: 99%

“…According to the analytical solutions, we then study the behavior of the wave propagation in quantum plasma and discover much more interesting linear and nonlinear structures of these equations. For this purpose, we will use the auxiliary equation method and Hirota bilinear method to study the QZK equation which derived by Moslem et al [14] from QHD model in this paper. Many types of new exact traveling wave solutions, which include smooth solitary wave, peakons, trigonometric periodic wave, doubly periodic wave solutions and multiple-soliton solutions are obtained.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New exact solitary wave and multiple soliton solutions of quantum Zakharov–Kuznetsov equation

Zhang

Liu

Xiao

2010

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New exact solitary wave and multiple soliton solutions of quantum Zakharov–Kuznetsov equation

Zhang

Liu

Xiao

2010

Applied Mathematics and Computation

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“…In addition, the ZK equation for fully degenerate plasma will have A = 4/3 and H = (1/2) ω pe /E F in coefficients B and C. The associated fully degenerate ZK equation does not match the results from Refs. [20][21][22], after comparison using physical (dimensional and nonstretched) coordinates, restricted to the case of electron-ion plasmas. Note that the ZK equations from the previous works do not match the purely classical result.…”

Section: Zakharov-kuznetsov Equation For Arbitrary Degeneracymentioning

confidence: 99%

“…The ZK equation is a multidimensional extension of the well-known Korteweg-de Vries equation for studying solitons (or single-pulse structures). In the degenerate magnetized plasma case, the cold Fermi electron gas assumption has been applied in the derivation of the appropriate ZK equation [20][21][22], restricted to the fully degenerate case of a negligible thermodynamic temperature in comparison to the Fermi temperature.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons

Haas

Mahmood

2016

Phys. Rev. E

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Nonlinear ion-acoustic waves are analyzed in a nonrelativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite-temperature quantum kinetic theory in the long-wavelength limit. The dispersion relation of the obliquely propagating electrostatic waves in magnetized quantum plasma with arbitrary degeneracy of electrons is obtained. Using the reductive perturbation method, the corresponding Zakharov-Kuznetsov equation is derived, describing obliquely propagating two-dimensional ion-acoustic solitons in a magnetized quantum plasma with degenerate electrons having an arbitrary electron temperature. It is found that in the dilute plasma case only electrostatic potential hump structures are possible, while in dense quantum plasma, in principle, both hump and dip soliton structures are obtainable, depending on the electron plasma density and its temperature. The results are validated by comparison with the quantum hydrodynamic model including electron inertia and magnetization effects. Suitable physical parameters for observations are identified.

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Excitation of nonlinear longitudinal structures in spin‐1/2 quantum plasma in the presence of ion beam

Iqbal,

Abbas,

Rozina

et al. 2024

Contrib. Plasma Phys

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The formation of longitudinal, nonlinear structures in an interacting ion beam, spin‐1/2 quantum, electron‐ion plasma is reported by employing a separate spin evolution quantum hydrodynamic model (SSE‐QHD). The reductive perturbation method is followed to develop the KdV equations. In the presence of an ion beam and keeping the finite electron inertial effects, ion acoustic (IA) soliton and spin electron acoustic (SEA) soliton are found. The critical values of beam speed and spin polarization, required for the existence of solitary structures, are highlighted. It is prescribed that the present model supports rarefactive and compressive SEA soliton and compressive IA soliton. It is shown that the ion beam is essential for the existence of a compressive SEA solitary structure. We have also calculated and compared the energy densities of both solitons. Furthermore, the dependence of the nonlinear structures on the beam parameters and spin polarization are also examined. Our findings would be useful to understand the new spin‐dependent nonlinear structures as well as the features of nonlinear IA waves in ion beam–plasma interactions.

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Solitary, explosive, and periodic solutions of the quantum Zakharov-Kuznetsov equation and its transverse instability

Cited by 115 publications

References 49 publications

New exact solitary wave and multiple soliton solutions of quantum Zakharov–Kuznetsov equation

New exact solitary wave and multiple soliton solutions of quantum Zakharov–Kuznetsov equation

Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons

Excitation of nonlinear longitudinal structures in spin‐1/2 quantum plasma in the presence of ion beam

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