  A self consistent theory of a cigar shaped Bose-Einstein condensate (BEC)
periodically modulated by a laser beam is presented. We show, both
theoretically and numerically, that modulational instability/stability is the
mechanism by which wavefunctions of soliton type can be generated in cigar
shaped BEC subject to a 1D optical lattice. The theory explains why bright
solitons can exist in BEC with positive scattering length and why condensate
with negative scattering length can be stable and give rise to dark solitary
pulses.
