  Dark and grey soliton-like states are shown to emerge from numerically
constructed superpositions of translationally-invariant eigenstates of the
interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics
reveals a density depression with superdiffusive spreading that is absent in
the mean-field treatment of solitons. A simple theory based on finite-size
bound states of holes with quantum-mechanical center-of-mass motion
quantitatively explains the time-evolution of the superposition states and
predicts quantum effects that could be observed in ultra-cold gas experiments.
The soliton phase step is shown to be a key ingredient of an accurate finite
size approximation, which enables us to compare the theory with numerical
simulations. The fundamental soliton width, an invariant property of the
quantum dark soliton, is shown to deviate from the Gross-Pitaevskii predictions
in the interacting regime and vanishes in the Tonks-Girardeau limit.
