  A one-dimensional model of bosons with repulsive short-range interactions,
solved analytically by Lieb and Liniger many years ago, predicts existence of
two branches of elementary excitations. One of them represents Bogoliubov
phonons, the other, as suggested by some authors, might be related to dark
solitons. On the other hand, it has been already demonstrated within a
framework of the classical field approximation that quasi-one-dimensional
interacting Bose gas at equilibrium exhibits excitations which are phonons and
dark solitons. By showing that statistical distributions of dark solitons
obtained within the classical field approximation match the distributions of
quasiparticles of the second kind derived from fully quantum description we
demonstrate that type II excitations in the Lieb-Liniger model are, indeed,
quantum solitons.
