A concentrated nuclear bulge with about 30% of the galaxy mass is sufficient (Lin, 1975; Berman and Mark, 1978) to eliminate strong bar-forming instabilities which dominate the dynamics of the stellar disk. Weak bar-like or oval distortions might remain depending on the model. In such systems self-excited discrete modes give rise to global spiral patterns which are maintained in the presence of differential rotation and dissipation (cf. especially the spiral patterns in Bertin et al., 1977, 1978). These spiral modes are standing waves that are physically analyzable (Mark, 1977) into a superposition of two travelling waves propagating in opposite directions back and forth between galactic central regions and corotation (a resonator). Only a few discrete pattern frequencies are allowed. An interpretation is that the central regions and corotation radius must be sufficiently far apart so that a Bohr-Sommerfeld type of phase-integral condition is satisfied for the wave system of each mode. The temporal growth of these modes is mostly due to an effect of Wave Amplification by Stimulated Emission (of Rotating Spirals, abbrev. WASERS, cf. Mark 1976) which occurs in the vicinity of corotation. In some galaxies one mode might be predominent while other galaxies could exhibit more complicated spiral structure because several modes are present. Weak barlike or oval distortions hardly interfere with the structure of these modes. But they might nevertheless contribute partially towards strengthening the growth of one mode relative to another, as well as affecting the kinematics of the gaseous component.
On a time fractional diffusion with nonlocal in time conditions