  We numerically investigate spherically symmetric collapses in the
Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential.
Even below threshold for direct collapse, the wave function bounces off from
the origin and may eventually become singular after a number of oscilla- tions
in the trapping potential. This is reminiscent of the evolution of Einstein
gravity sourced by a scalar field in Anti-de Sitter space where collapse
corresponds to black hole formation. We carefully examine the long time
evolution of the wave function for continuous families of initial states in
order to sharpen out this qualitative coincidence which may bring new insights
in both directions. On one hand, we comment on possible implications for the
so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the
other hand, Gross-Pitaevskii provides a toy model to study the relevance of
either the resonance conditions or the nonlinearity for the problem of Anti-de
Sitter instability.
