  Describing properties of a strongly interacting quantum many-body system
poses a serious challenge both for theory and experiment. In this work, we
study excitations of one-dimensional repulsive Bose gas for arbitrary
interaction strength using a hydrodynamic approach. We use linearization to
study particle (type-I) excitations and numerical minimization to study hole
(type-II) excitations. We observe a good agreement between our approach and
exact solutions of the Lieb-Liniger model for the particle modes and
discrepancies for the hole modes. Therefore, the hydrodynamical equations find
to be useful for long-wave structures like phonons and of a limited range of
applicability for short-wave ones like narrow solitons. We discuss potential
further applications of the method.
