“…To describe dust acoustic solitons (see, e.g., [13][14][15]), the following set of equations can be used, which includes the continuity equation, the (Euler) motion equation for the dust grains, and Poisson's equation for the self-consistent electrostatic potential in the dusty plasma of Saturn's magnetosphere: (1) where the space variable x corresponds to the propagation direction of the wave perturbation, n d is the concentration of dust grains, is their velocity, m d and q d = Z d e is the mass and charge of dust grains, is the electron charge, n e,c(h) is the concentration of hot (cold) electrons, and n i is the concentration of ions.…”