  We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb
atoms placed in an optical waveguide. The number of localized spatial
components observed in the breakup is compared with the number of solitons
predicted by a plane-wave stability analysis of the nonpolynomial nonlinear
Schr\"odinger equation, an effective one-dimensional approximation of the
Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the
numbers predicted from the fastest growing sidebands are consistent with the
experimental data, suggesting that modulational instability is the key
underlying physical mechanism driving the breakup.
