  The interaction of nonlinear Schr\"{o}dinger (NLS) solitons with potential
wells with variable shapes is investigated numerically. For fixed initial
velocities below the threshold for transmission, the outcome pattern as a
function of the width of the potential yields periodically repeating regions of
trapping, transmission and reflection. The observed effects are explained by an
excitation and a following resonant deexcitation of amplitude (shape)
oscillations of the solitons at the boundaries of the well, associated with
radiation modes.
