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

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