  We study the dynamical phase diagram of a dilute Bose-Einstein condensate
(BEC) trapped in a periodic potential. The dynamics is governed by a discrete
non-linear Schr\"odinger equation: intrinsically localized excitations,
including discrete solitons and breathers, can be created even if the BEC's
interatomic potential is repulsive. Furthermore, we analyze the
Anderson-Kasevich experiment [Science 282, 1686 (1998)], pointing out that mean
field effects lead to a coherent destruction of the interwell Bloch
oscillations.

Statistical Mechanics;Mesoscale and Nanoscale Physics;Soft Condensed Matter;Superconductivity