  We study the dynamics of a Bose-Einstein condensate (BEC) in a one
dimensional optical lattice in the limit of weak atom-atom interactions.
Numerically we find that a BEC may develop a pulsating instability in which
atoms nearly periodically collect themselves into a pulse and subsequently
disperse back into the initial homogeneous state. A qualitative explanation of
the quasi-periodic behavior is given by drawing an analogy with a double-well
system. In an extension we introduce quantum effects approximately within
Truncated Wigner Approximation (TWA). In pure classical mean field theory the
condensate shows an undamped pulsating instability, whereas we have observed a
damping in the oscillation when we average over many stochastic realizations.
