Zakharov–Kuznetsov Equation for Describing Low-Frequency Nonlinear Dust Acoustic Perturbations in Saturn’s Dusty Magnetosphere

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Abstract

A description is given of low-frequency nonlinear dust acoustic waves in Saturn’s dusty magnetosphere, which contains electrons of two types (hot and cold) obeying the kappa distribution, magnetospheric ions, and charged dust particles. For the corresponding conditions, the derivation of the Zakharov–Kuznetsov equation is given, which describes the nonlinear dynamics of dust acoustic waves in the case of low frequencies and a pancake-shaped wave packet along an external magnetic field. It is shown that under the conditions of Saturn’s magnetosphere there exist solutions of the Zakharov–Kuznetsov equation in the form of one-dimensional and three-dimensional solitons. Possible observations of the considered solitons in future space missions are discussed.

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About the authors

S. I. Kopnin

Space Research Institute, Russian Academy of Sciences

Email: popel@iki.rssi.ru
Russian Federation, Moscow

D. V. Shokhrin

Higher School of Economics

Email: popel@iki.rssi.ru
Russian Federation, Moscow

S. I. Popel

Space Research Institute, Russian Academy of Sciences

Author for correspondence.
Email: popel@iki.rssi.ru
Russian Federation, Moscow

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2. Fig. 1. Characteristic view of one-dimensional solitons propagating at the angle J to the magnetic field: J = 1° - solid curve, J = 3° - dashed curve, J = 5° - dashed curve. The graphs are plotted for three cases of possible dust particle concentrations: nd0 = 10-4 cm-3 (a), nd0 = 10-3 cm-3 (b), nd0 = 10-2 cm-3 (c)

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3. Fig. 2. Moduli of the amplitudes of the soliton solutions (67) as a function of the characteristic mean dust particle sizes a and the soliton propagation velocity u at J = 5° for nd0 = 10-4 cm-3 (a), nd0 = 10-3 cm-3 (b), nd0 = 10-2 cm-3 (c)

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4. Fig. 3. Three-dimensional soliton for the cases: nd0 = 10-2 cm-3 (a), nd0 = 10-3 cm-3 (b), nd0 = 10-4 cm-3 (c)

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