Prog. Theor. Phys. Vol. 55 No. 5 (1976) pp. 1419-1431
Nonlinear Modulation of Density Wave in Self-Gravitating Systems
— Gas Dynamical Description
Department of Physics, Kyoto University, Kyoto 606
(Received October 21, 1975)
Nonlinear modulation of density wave in self-gravitating systems is
studied by the reductive perturbation method. Using gas dynamical
equations, an infinitely long rotating cylinder and an infinitesimally
thin disk are considered. In the former system, both one-dimensional
and two-dimensional modulations, the so-called self-focusing, are
found to be stable for all wave number when the carrier wave
propagates perpendicularly to rotational axis. In the latter system,
amplitude modulation becomes unstable for large wave number. This
unstable amplitude modulation grows to the envelope solitary wave in a
time of the order of rotational one even if the amplitude of carrier
wave is as low as one hundredth of zeroth order quantity.
It is concluded that nonlinear effects cannot be neglected in the density wave theory of spiral arms. The conjecture is proposed that this nonlinear modulationally unstable mode can be identified with the spiral arms of S-type galaxies.
DOI : 10.1143/PTP.55.1419
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Citing Article(s) :
Progress of Theoretical Physics Vol. 57 No. 4 (1977) pp. 1239-1254
Resonant Three-Wave Interactions of Density Waves in a Self-Gravitating Disk