  By solving the Gross-Pitaevskii equation analytically and numerically, we
reexamine the implosion phenomena that occur beyond the critical value of the
number of atoms of an attractive Bose-Einstein condensate (BEC) with
cigar-shape trapping geometry. We theoretically calculate the critical number
of atoms in the condensate by using Ritz's variational optimization technique
and investigate the stability and collapse dynamics of the attractive BEC by
numerically solving the time dependent Gross-Pitavskii equation.
