  We investigate the problem of self-gravitating dust disk dynamics in a static
state taking into account nonlinear effects. For this purpose Schrodinger-type
equation including the mass conservation law is used for the whole description
of hydrodynamic flows of self-gravitating dust. We have shown a purely
hydrodynamic mechanism of ring formation in the radial direction by taking into
account nonlinearity in the lowest order of expansion parameter, which
determines an order of magnitude of flow.

Astrophysics