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.