Excluding the instability of the infinite uniform medium investigated by J.Jeans in the early this century, all the other instabilities of the observed gravitating systems known up today (more than 10) were found and studied by the authors. In particular, the radial orbit instability which is one of the principal instabilities of collisionless stellar systems was discovered by Polyachenko and Shukhman.
Contrary to the wide-spread opinion that a collapse of gravitating perturbations occurs with wavelengths larger than certain critical value, we pointed to a new class "asynphase" eigen oscillations existing in real multi-component gravitating medium as non-collapsing waves with an arbitrary large wavelength; this phenomenon would be impossible in one-component medium.
It was first shown that the solitons can exist in gravitating systems, and they can be transformed into the "gravity" shock waves by presence of dissipation. Against the traditional opinion that the shock wave are impossible in stellar systems (as the latter are collisionless), we proved that such waves can be in rotating stellar disks, with the epicycle size playing a role of the mean free path length. The possibility of existence of the Landau non-linear damping was first demonstrated.
A weak turbulence theory for rotating gravitational systems was developed; the observed correlations between the main parameters of gas clouds and their structures in the Galaxy (and also the Salpeter mass spectrum for stars) were resulted from this theory.
For the first time the correct 2-D nonlinear equation describing the dynamics of large-scale slow perturbations of gaseous astrophysical discs is derived. We show, that stationary solutions of this equation correspond to solitary and double vortices, that are similar to Rossby solitons in ocean and atmosphere.
The studies of the rotation curves of spiral galaxies with the 6-meter telescope were first made by our collaborators. This work revealed "jumps" and "kinks" on rotation velocity curves of the majority of galaxies; these rotation peculiarities are sufficient for development of the hydrodynamical instabilities that were proposed by us as one of the main generators of the spiral-vortex structure of galaxies.
In addition to the well-known galactic fast bars, the occurrence of slow bars in spiral galaxies were proved; such bars are formed by the mutual contraction and merging of slowly precessing elongated orbits of stars.
Above results were obtained by A.M.Fridman, V.L.Polyachenko, O.V.Khoruzhii, V.V.Lyakhovich