  We present a numerical study of the dynamical effects following a sudden
change of the transverse trapping frequency in an elongated Bose-Einstein
condensate, which induces periodic oscillations of the radial density. At early
times, we observe an exponential growth of the number of resonant longitudinal
phonons, in agreement with the predictions of the Bogoliubov-de Gennes
treatment. We then observe an ordered sequence of phenomena induced by the
nonlinearities of the system. The first is a loss of the nonseparability of the
resonant phonon pairs. This is followed by the saturation of the exponential
growth and a strong depletion of condensed atoms. Notably, these effects are
well-described by effective 1D dynamics, and are hardly affected by the damping
of the radial oscillations. Finally, the atomic spectrum becomes broad,
featureless and almost incoherent, in agreement with experimental results. The
link between this sequence of events and the preheating scenario in
inflationary cosmology is striking, as is the similarity of techniques used to
study them.
