The Waves on the Vortex Ring in HeII

Using the equations of vortex dynamics the waves on a vortex ring are studied both analytically and by computer simulations. At small amplitudes the results coincide. The dispersion relations and the expressions of phase and group velocities are determined. The free and forced oscillations are considered. At large amplitudes the shape of a vortex is strongly distorted and the ring motion changes its direction. The second approximation calculations and computer simulations agree in order of magnitude.