Resonant Three-Wave Interactions of Density Waves in a Self-Gravitating Disk

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Abstract
As a nonlinear behavior of density wave in a self-gravitating disk, resonant three-wave processes are discussed. For both cases of the hydrodynamical and the Vlasov description of the disk, the resonance condition and the coupling coefficients of parametric interactions are calculated. When the wave duration time is so small, the steady propagation of triple solitary pulses is expected. The conditions for this mode are examined for a disk-like galaxy and the soliton model of spiral arms is discussed.

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