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We continue the study of dispersive quantum shock waves in a one-dimensionalBose gas beyond the mean-field approximation. In a recent work by Simmons etal. [Phys. Rev. Let. 125, 180401 (2020)], the oscillatory shock wave traindeveloping in this system from an initial localized density bump on a uniformbackground was interpreted as a result of quantum mechanical self-interference,wherein the interference contrast would diminish with the loss of matter-wavephase coherence. Such loss of coherence, relative to the mean-fieldGross-Pitaevskii description, occurs due to either quantum or thermalfluctuations, as well as in the strongly interacting regime. In this work, weextend the analysis of dispersive quantum shock waves in this context to otherdynamical scenarios. More specifically, the scenarios studied include evolutionof a sufficiently high density bump, known to lead to the so-called ``vacuumpoint'' 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. Westudy the fate of these nonlinear wave structures in the presence of quantumand thermal fluctuations, as well as at intermediate and strong interactions,and show that both the vacuum point and grey solitons cease to manifestthemselves beyond the mean-field approach. On the other hand, we find that avacuum point can occur in an ideal (noninteracting) Bose gas evolving from aground state of a localized dimple potential. Due to the ubiquity of dispersiveshock waves in nature, our results should provide useful insights andperspectives for a variety of other physical systems known to display nonlinearwave phenomena.

Fate of the "vacuum point'' and of grey solitons in dispersive quantum shock waves in a one-dimensional Bose gas