  We present a two-dimensional nonlinear equation to govern the dynamics of
disturbances in a rotating self-gravitating fluid. The nonlinear term of the
equation has the form of a Poisson bracket (Jacobian), and the linear part
contains, along with the Laplacian, a biharmonic operator. A solution was found
in the form of a dipole vortex (modon). The solution and all its derivatives up
to the fourth order are continuous on the separatrix.
