Dispersive shock waves in one-dimensional quantum droplets

We explore dispersive hydrodynamic phenomena in quantum droplets of homonuclear cold bosonic mixtures utilizing an extended Gross-Pitaevskii framework. This model supports various self-bound configurations such as droplets, bubbles and kinks. It is shown that the interaction of these structures can lead to the dynamical nucleation of dispersive shock-waves. We unravel the dispersive regularization of hydrodynamic singularities in these systems due to the competition of mean-field repulsion and quantum fluctuation attraction. Interestingly, the controllable generation of dispersive shock-waves with the aid of initial state engineering is demonstrated. This can be understood in terms of families of Riemann problems. We classify and analyze the emergent wave-patterns using Whitham modulation theory.