  Interactions of solitary waves in a cylindrically confined Bose-Einstein
condensate are investigated by simulating their head-on collisions. Slow vortex
rings and fast solitons are found to collide elastically contrary to the
situation in the three-dimensional homogeneous Bose gas. Strongly inelastic
collisions are absent for low density condensates but occur at higher densities
for intermediate velocities. The scattering behaviour is rationalised by use of
dispersion diagrams. During inelastic collisions, spherical shell-like
structures of low density are formed and they eventually decay into depletion
droplets with solitary wave features. The relation to similar shells observed
in a recent experiment [Ginsberg et al. Phys Rev. Lett. 94, 040403 (2005)] is
discussed.
