Nonlinear stability theory for a rotating gravitating disk
Abstract
A nonlinear equation is derived for a wave of small but finite amplitude propagating in the plane of a rotating gravitating gas disk. It is shown that depending on the equation of state and the nature of the waves, this equation may describe the disruptive instability or may have a steadystate solitontype solution. The solitons are found to be either supersonic or subsonic, depending on the equation of state. The results indicate that supersonic solitons may occur and propagate only in the case of weak Jeans instability of the disk, while subsonic solitons may propagate only in a stable (in the Jeans sense) disk. It is concluded that the disruptive instability may develop both in a stable disk and against the background of the Jeans instability.
 Publication:

Astronomicheskii Zhurnal
 Pub Date:
 April 1979
 Bibcode:
 1979AZh....56..279M
 Keywords:

 Galactic Rotation;
 Gravitational Fields;
 Jeans Theory;
 Rotating Disks;
 Differential Equations;
 Dynamic Stability;
 Fourier Series;
 Interstellar Gas;
 Milky Way Galaxy;
 Nonlinear Equations;
 Solitary Waves;
 Wave Equations;
 Wave Propagation;
 Astrophysics