Resonantly Excited Non-linear Density Waves in Disk Systems

Most of the disk systems are characterized by spiral structures. A good portion of these spiral structures can be identified as waves resonantly excited by a perturber in or pertaining to the same system. For planetary rings, this is an exterior satellite; for galactic disks, a rotating bar; for proto-stellar disks (yet to be confirmed), this would be a proto-planet. These waves, not just responsible for the present morphology of the disks, also play a dominating role on evolution of the disks. Resonance excitation is a extremely effective mechanism. A relatively weak perturbation can result in a highly non-linear responses in the disk. Therefore, non-linear theory is a necessity here. We will examine the non-linear theory of resonance excitation and discuss the applications of the theory to Saturn's rings and disk galaxies in this paper.