Two-Dimensional Description of Nonlinear Wave Perturbations in the Dusty Saturn’s Magnetosphere

Two-dimensional description of nonlinear dust-acoustic waves in the dusty Saturn’s magnetiosphere that contains electrons of two types (the hot and the cold ones) obeying the kappa distribution, along with magnetospheric ions and charged dust particles, is presented. The Kadomtsev–Petviashvili equation that describes the nonlinear dynamics of the nearly one-dimensional wave structures is derived for the conditions of the dusty Saturn’s magnetosphere. The possibility of propagation of localized wave structures of the dust-acoustic soliton type is analyzed. It is demonstrated that the Kadomtsev–Petviashvili equation has solutions in the form of one-dimensional solitons and two-dimensional N-solitons under the conditions of the Saturn’s magnetosphere. The possibility of observation of the discussed solitons during future space missions is discussed.