Hyper-Riccati equations and integrable reductions permitting stationary solutions for complex hyperbolic field equations

Theaker, Kyle A.; Gorder, Robert A. Van

doi:10.1016/j.amc.2013.03.004

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…In these models, the coefficients have different meanings, but mathematically the results are the same. This type of equation was studied by Theaker et al [51]. For the case of a more general-degree polynomial, some relations with quantum field theory have been made.…”

Section: Zakharov-kuznetsov Equationmentioning

confidence: 99%

Role of superthermality on dust acoustic structures in the frame of a modified Zakharov–Kuznetsov equation in magnetized dusty plasma

Sabetkar

Dorranian

2015

Phys. Scr.

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In this paper, a theoretical investigation is presented to study the existence and characteristics of the propagation of dust acoustic (DA) waves in an obliquely propagating magnetized dusty plasma with two populations of ions having two distinct temperatures, electrons that are modeled by three-dimensional nonextensive and κ-distribution functions, respectively, and negative dust particles. Normal mode analysis (reductive perturbation method) is used to derive lower-and higher-order nonlinear equations governing the evolution of small but finite amplitude DA waves, namely the Zakharov-Kuznetsov (ZK) and the modified Zakharov-Kuznetsov (mZK) equations. The basic features (e.g., amplitude, width, phase speed, polarity) of both DA ZK and mZK solitons have been thoroughly examined by the numerical analysis of their equations. It is observed that the characteristics and properties of the DA solitary waves (DASWs) are significantly modified by the superthermality of electrons, nonextensivity of ions, cold-to-hot ion temperature ratio, relative number densities of two species of ions, and the strength of the magnetic field and obliqueness of the system. Furthermore, it has been found that the DA ZK solitons exhibit only negative polarity of solitary waves when the superthermality of electrons, nonextensivity of ions, and temperature ratio of ions are smaller or greater than their critical values. The present study may add to the understanding of the nonlinear propagation features of DA wave structures in high-energy astrophysical plasma systems.

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Section: Zakharov-kuznetsov Equationmentioning

confidence: 99%