1994A&A...290..785D

We use N-body simulations to study the non-linear evolution of spontaneous and tidally induced spiral patterns in galaxies on time-scales of several rotation periods of the disc. We find that the patterns can sometimes survive with an almost constant amplitude for five revolutions or more, and tend to be regenerated after disappearing temporarily. The pattern velocity is such that the corotation radius is where the self-gravity as measured by the swing amplification of the m=2 component is strongest, and the amplitude of the pattern is larger when swing amplification is stronger. The shape of the spirals is independent of the origin of the pattern, and corresponds to the critical wave number κ²/(2πGµ), where µ is the disc surface density. The pattern survives longer if the self-gravity of the disc is strong. For a given disc model the life-time of the pattern depends on its amplitude, with stronger patterns having shorter life-times. If self-gravity is weak, the dominant tidal effect is a kinematic spiral at the inner Lindblad resonance.