  Mean-field dynamics of strongly interacting bosons described by hard core
bosons with nearest-neighbor attraction has been shown to support two species
of solitons: one of Gross-Pitaevskii (GP-type) where the condensate fraction
remains dark and a novel non-Gross-Pitaevskii-type (non-GP-type) characterized
by brightening of the condensate fraction. Here we study the effects of quantum
fluctuations on these solitons using the adaptive time-dependent density matrix
renormalization group method, which takes into account the effect of strong
correlations. We use local observables as the density, condensate density and
correlation functions as well as the entanglement entropy to characterize the
stability of the initial states. We find both species of solitons to be stable
under quantum evolution for a finite duration, their tolerance to quantum
fluctuations being enhanced as the width of the soliton increases. We describe
possible experimental realizations in atomic Bose Einstein Condensates,
polarized degenerate Fermi gases, and in systems of polar molecules on optical
lattices.
