  Coherent transverse oscillations of a bunch in a ring accelerator are
considered. Three different models of the bunch are used: a hollow bunch in a
square potential well, a square bunch in a parabolic potential well, and a
parabolic bunch in a parabolic well. The bunch space-charge field, wakefield,
and chromaticity are taken into account in all the cases. The bunch eigenmodes
and various instabilities are studied. The results are compared and analyzed to
establish the range of applicability of the models. Role of the Landau damping
due to dependence of the SC field on the longitudinal coordinate is discussed.
