  Schr\"odinger equation for Bose gas with repulsive contact interactions in
one-dimensional space may be solved analytically with the help of the Bethe
ansatz if we impose periodic boundary conditions. It was shown that in such a
system there exist many-body eigenstates directly corresponding to dark soliton
solutions of the mean-field equation. The system is still integrable if one
switches from the periodic boundary conditions to an infinite square well
potential. The corresponding eigenstates were constructed by M. Gaudin. We
analyze weak interaction limit of Gaudin's solutions and identify
parametrization of eigenstates strictly connected with single and multiple dark
solitons. Numerical simulations of detection of particle's positions reveal
dark solitons in the weak interaction regime and their quantum nature in the
presence of strong interactions.
