Mathematics
Scientific paper
Feb 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979stam...60...11n&link_type=abstract
Studies in Applied Mathematics, vol. 60, Feb. 1979, p. 11-26. Research supported by the Ministry of Education of Japan and NSF.
Mathematics
3
Astronomical Models, Density Wave Model, Disk Galaxies, Wave Dispersion, Angular Velocity, Asymptotic Methods, Boundary Value Problems, Cubic Equations, Differential Equations, Polynomials, Wentzel-Kramer-Brillouin Method
Scientific paper
The paper presents an asymptotic form of the global dispersion relation for a cubic polynomial differential equation for density waves in a simplified model of a disk shaped galaxy. The stability parameter in this equation is permitted to be less than unity near corotation. It was shown that discrete complex roots of the dispersion relation exist with small negative imaginary parts; the real and imaginary parts of these roots approximately represent the angular speeds and the growth rate of the amplitudes of the waves. Finally, it was proved that there is only a finite number of unstable modes of density waves.
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