Propagation properties and stability of dark solitons in weakly interacting Bose-Bose droplets

We investigate dark solitons in two-component Bose systems with competing interactions in one dimension. Such a system hosts a liquid phase stabilized by the beyond-mean field corrections. Using the generalized Gross-Pitaevskii equation, we reveal the presence of two families of solitonic solutions. The solitons in both of them can be engineered to be arbitrarily wide. One family of solutions, however, has got an anomalous dispersion relation and our analyses show one of its branches is unstable. We find the presence of a critical velocity demarcating the stable from unstable solutions. Nonetheless, grey anomalous solitons are able to exist inside quantum droplets and can be treated as solitonic excitations thereof.