  We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous
dispersive imaging by using a Lindblad operator formalism. Continuous strong
measurements drive the condensate out of the coherent state description assumed
within the Gross-Pitaevskii mean-field approach. Continuous weak measurements
allow instead to replace, for timescales short enough, the exact problem with
its mean-field approximation through a stochastic analogue of the
Gross-Pitaevskii equation. The latter is used to show the unwinding of a dark
soliton undergoing a continuous imaging.
