Pulse propagation in the interacting one-dimensional Bose liquid

We study wave propagation in interacting Bose liquid, where the short-range part of the interaction between atoms is of a hard-core type, and its long-range part scales with a distance as a power law. The cases of Coulomb, dipole-dipole and van der Waals interaction are considered. We employ a hydrodynamic approach, based on the exact solution of the Lieb--Liniger model, and study the evolution of a density pulse instantly released from a potential trap. We analyze semiclassical Euler and continuity equations and construct the corresponding Riemann invariants. We supplement our analysis with numerical calculations and discuss experimental applications for ultracold atom experiments.