  Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic
mirror) under the effect of gravity has been studied by analytical and
numerical means. The analytical description is based on the variational
approach. Resonant oscillations of the soliton's center of mass and width,
induced by appropriate modulation of the atomic scattering length and the slope
of the linear potential are analyzed. In numerical experiments we observe the
Fermi type acceleration of the soliton when the vertical position of the
reflecting surface is periodically varied in time. Analytical predictions are
compared with the results of numerical simulations of the Gross-Pitaevskii
equation and qualitative agreement between them is found.
