  We study solitary wave propagation in the condensate of a system of hard-core
bosons with nearest-neighbor interactions. For this strongly repulsive system,
the evolution equation for the condensate order parameter of the system,
obtained using spin coherent state averages is different from the usual
Gross-Pitaevskii equation (GPE). The system is found to support two kinds of
solitons when there is a particle-hole imbalance: a dark soliton that dies out
as the velocity approaches the sound velocity, and a new type of soliton which
brightens and persists all the way up to the sound velocity, transforming into
a periodic wave train at supersonic speed. Analogous to the GPE soliton, the
energy-momentum dispersion for both solitons is characterized by Lieb II modes.
