Eigenstates of Bose particles with repulsive contact interactions in
one-dimensional space with periodic boundary conditions can be found with the
help of the Bethe ansatz. The type~II excitation spectrum identified by E. H.
Lieb, reproduces the dispersion relation of dark solitons in the mean-field
approach. The corresponding eigenstates possess translational symmetry which
can be broken in measurements of positions of particles. We analyze emergence
of single and double solitons in the course of the measurements and investigate
dynamics of the system. In the weak interaction limit, the system follows the
mean-field prediction for a short period of time. Long time evolution reveals
many-body effects that are related to an increasing uncertainty of soliton
positions. In the strong interaction regime particles behave like impenetrable
bosons. Then, the probability densities in the configuration space become
identical to the probabilities of non-interacting fermions but the
wave-functions themselves remember the original Bose statistics. Especially,
the phase flips that are key signatures of the solitons in the weak interaction
limit, can be observed in the time evolution of the strongly interacting
bosons.Comment: 11 pages, 9 figure
