Quasi-solitons of the 1D Bose gas at arbitrary-strength contact repulsion

Harnessing integrability at arbitrary interaction strength, we build long-lived and spatially localized soliton-like excitations in the 1D Bose gas with contact repulsion (Lieb-Liniger model). We show how these density profiles, built from selective superpositions of multi-hole eigenstates, display long lifetimes tunable through parameters like dispersion width and number of holes. We further illustrate a scaling protocol that in principle enables unbounded increase in lifetimes in the thermodynamic limit. Our results showcase classical-like excitations originating from unitary quantum dynamics, away from the semi-classical regime, and in regions where interactions cannot be treated perturbatively.