  Employing the Bethe ansatz approach and numerical simulations of measurements
of particles' positions we investigate a post-quench many-body dynamics of
attractively interacting bosons on a ring, which in the mean-field approach
corresponds to the so-called breather solution. Despite the fact that the
initial many-body ground state is translationally invariant, the measurements
reveal breather dynamics if quantum fluctuations of the center of mass of the
system are extracted. Moreover, the analysis of the many-body evolution shows
signatures of dissociation of the solitons that form the breather.
