  The stability of an attractive Bose-Einstein condensate on a joint
one-dimensional optical lattice and an axially-symmetric harmonic trap is
studied using the numerical solution of the time-dependent mean-field
Gross-Pitaevskii equation and the critical number of atoms for a stable
condensate is calculated. We also calculate this critical number of atoms in a
double-well potential which is always greater than that in an axially-symmetric
harmonic trap. The critical number of atoms in an optical trap can be made
smaller or larger than the corresponding number in the absence of the optical
trap by moving a node of the optical lattice potential along the axial
direction of the harmonic trap. This variation of the critical number of atoms
can be observed experimentally and compared with the present calculation.
