We compute by quadrature all soliton solutions of the unforced lossless 1D coupled exciton-polariton equations.

Repulsive nonlinearity allows two bands of dark solitons, and attractive nonlinearity allows two bands of bright solitons.

There are discontinuous solitons—one dark band and a band with dark photon field and bright exciton field.

Bright solitons have stable far fields, whereas dark solitons have both stable (lower band) and unstable (upper band) far fields.