Mathematics
Scientific paper
Aug 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981stam...65....1y&link_type=abstract
(American Astronomical Society, Meeting, 154th, Wellesley, MA, June 10-14, 1979.) Studies in Applied Mathematics, vol. 65, Aug.
Mathematics
1
Galactic Evolution, Gravitational Waves, Nonlinear Equations, Solitary Waves, Wave Dispersion, Wave Equations, Density Wave Model, Electron Gas, Magnetohydrodynamic Stability, Plasma Waves, Shock Wave Propagation
Scientific paper
Exact solutions of nonlinear waves are obtained in order to study the effects of finite amplitudes on the behavior of waves in a self-gravitating medium. The waves are assumed to travel in the direction of the axis of rotation of a homogeneous and uniformly rotating self-gravitating medium. The nonlinear wave profile and the dispersion relation are obtained and compared with Jeans' nonlinear theory. It is found that the wavelength-amplitude plane can be divided into three regions: (1) a region where the shock wave is expected to form, (2) a region where the neutral wave exists, and (3) a region where there is gravitational instability. In the third case, it is expected that the unstable wave will eventually evolve to a neutral wave with finite amplitude. Based on this result, the evolution of an unstable density wave in a galaxy is considered. It is shown that the propagation of the nonlinear wave in a self-gravitating medium is always 'subsonic,' just as in the linear theory.
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