  The dark soliton created in a Bose-Einstein condensate becomes grey in course
of time evolution because its notch fills up with depleted atoms. This is the
result of quantum mechanical calculations which describes output of many
experimental repetitions of creation of the stationary soliton, and its time
evolution terminated by a destructive density measurement. However, such a
description is not suitable to predict the outcome of a single realization of
the experiment were two extreme scenarios and many combinations thereof are
possible: one will see (1) a displaced dark soliton without any atoms in the
notch, but with a randomly displaced position, or (2) a grey soliton with a
fixed position, but a random number of atoms filling its notch. In either case
the average over many realizations will reproduce the mentioned quantum
mechanical result. In this paper we use N-particle wavefunctions, which follow
from the number-conserving Bogoliubov theory, to settle this issue.
