On nonlinear spiral density waves

To overcome some difficulties encountered in the linear wave theory of galactic spiral structures interpreted as density waves, the present paper takes into account the nonlinear interaction of waves. The system of equations of hydrodynamics and gravitation is reduced to a hyperbolic system for the case of the gravitational field in a disk containing a central body (bulge). Such distribution of the density of matter is particularly typical of the 'early' Sa and Sb galaxies. It is shown that nonlinear density waves can exist in a self-gravitating differentially rotating thin disk with the gas distribution corresponding to that in disk galaxies with a central bulge. The principal characteristics of these waves are described.