  We study the formation and the subsequent dynamics of shock waves in
repulsive one-dimensional Bose gases during the free expansion of a density
hump. By building coherent Fermi states for interacting Bethe fermions, we
define a quantum fluctuating initial state expressed in terms of universal
quantities, namely the density and the Luttinger parameter. In the integrable
case, this fluctuating state is then evolved by generalized hydrodynamics (GHD)
and, differently from non-fluctuating initial states, it develops density
ripples on top of the hydrodynamic mean value. Our analysis gives a general
theory of quantum ripples and wave breaking in integrable and quasi-integrable
one-dimensional liquids and clarifies the role of the interaction strength. In
particular, for strongly/intermediately interacting bosons, we find quantum
ripples originating from low-energy modes at the Fermi surface interfering when
transported by GHD. In the low coupling limit, near the quasicondensate regime,
we find instead that density ripples have a semi-classical nature, and their
description requires information on the curvature of the Fermi surface.
