  Bose-Einstein condensates loaded into kicked optical lattices can be treated
as quantum kicked rotor systems. Noninteracting rotors show dynamical
localization in momentum space. The experimentally tunable condensate
interaction is included in a qualitative Gross-Pitaevskii type model based on
two-body interactions. We observe strong and weak chaos regimes of wave packet
spreading in momentum space. In the intermediate strong chaos regime the
condensate energy grows as $t^{1/2}$. In the asymptotic weak chaos case the
growth crosses over into a $t^{1/3}$ law. The results do not depend on the
details of the kicking.
