  Bose-Einstein condensates of exciton-polaritons are described by a
Schr\"odinger system of two equations. Nonlinearity due to exciton interactions
gives rise to a frequency band of dark soliton solutions, which are found
analytically for the lossless zero-velocity case. The soliton's far-field value
varies from zero to infinity as the operating frequency varies across the band.
For positive detuning (photon frequency higher than exciton frequency), the
exciton wavefunction becomes discontinuous when the operating frequency exceeds
the exciton frequency. This phenomenon lies outside the parameter regime of
validity of the Gross-Pitaevskii (GP) model. Within its regime of validity, we
give a derivation of a single-mode GP model from the initial Schr\"odinger
system and compare the continuous polariton solitons and GP solitons using the
healing length notion.
