  We study the dynamics of a Bose-Einstein condensate in a one-dimensional
optical lattice in the limit of weak atom-atom interactions, including an
approximate model for quantum fluctuations. A pulsating dynamical instability
in which atoms periodically collect together and subsequently disperse back
into the initial homogeneous state may occur in the time evolution. We take
into account the quantum fluctuations within the truncated Wigner
approximation. We observe that the quasiperiodic behavior still persists for a
single realization that represents a typical experimental outcome, but ensemble
averages show various manifestations of quantum fluctuations. Quantum effects
become more prominent when the effective interaction strength is increased.
