  We study how dark solitons, i.e. solutions of one-dimensional single-particle
nonlinear time-dependent Schr\"odinger equation, emerge from eigenstates of a
linear many-body model of contact interacting bosons moving on a ring, the
Lieb-Liniger model. This long-standing problem was addressed by various groups,
which presented different, seemingly unrelated, procedures to reveal the
solitonic waves directly from the many-body model. Here, we propose a
unification of these results using a simple Ansatz for the many-body eigenstate
of the Lieb-Liniger model, which gives us access to systems of hundreds of
atoms. In this approach, mean-field solitons emerge in a single-particle
density through repeated measurements of particle positions in the Ansatz
state. The post-measurement state turns out to be a wave packet of yrast states
of the reduced system.
