  In this work I introduce a powerful analytical method to analyze states of
non-equilibrium polariton Bose-Einstein condensates (BEC). It is shown that the
condensate wave functions carrying dark solitons and half-dark solitons can be
expressed in terms of the natural parameters of the non-equilibrium system,
i.e. the growth and decay rates and the interaction parameters. The derivation
is based on a non-conservative Lagrangian formalism, which provides ordinary
differential equations for the parameters of the dark soliton solutions in
their dynamic environment. Explicit expressions for the stationary solution are
stated, which significantly differ from those observed in atomic BEC.
Subsequently the method is extended to spinor condensates, which yields
ordinary differential equations for the parameters of half-dark solitons.
Finally a stationary case with explicit expressions for half-dark solitons is
presented as well.
