  We continue the study of dispersive quantum shock waves in a one-dimensional
Bose gas beyond the mean-field approximation. In a recent work by Simmons et
al. [Phys. Rev. Let. 125, 180401 (2020)], the oscillatory shock wave train
developing in this system from an initial localized density bump on a uniform
background was interpreted as a result of quantum mechanical self-interference,
wherein the interference contrast would diminish with the loss of matter-wave
phase coherence. Such loss of coherence, relative to the mean-field
Gross-Pitaevskii description, occurs due to either quantum or thermal
fluctuations, as well as in the strongly interacting regime. In this work, we
extend the analysis of dispersive quantum shock waves in this context to other
dynamical scenarios. More specifically, the scenarios studied include evolution
of a sufficiently high density bump, known to lead to the so-called ``vacuum
point'' in the mean-field description, and evolution of an initial density dip,
known to shed a train of grey solitons in the same mean-field approximation. We
study the fate of these nonlinear wave structures in the presence of quantum
and thermal fluctuations, as well as at intermediate and strong interactions,
and show that both the vacuum point and grey solitons cease to manifest
themselves beyond the mean-field approach. On the other hand, we find that a
vacuum point can occur in an ideal (noninteracting) Bose gas evolving from a
ground state of a localized dimple potential. Due to the ubiquity of dispersive
shock waves in nature, our results should provide useful insights and
perspectives for a variety of other physical systems known to display nonlinear
wave phenomena.
