  The formation of nonlinear Bloch states in open driven-dissipative system of
exciton-polaritons loaded into a weak-contrast 1D periodic lattice is studied
numerically and analytically. The condensate is described within the framework
of mean-field theory by the coupled equations for the order parameter and for
the density of incoherent excitons. The stationary nonlinear solutions having
the structure of Bloch waves are studied in detail. It is shown that there is a
bifurcation leading to the appearance of a family of essentially nonlinear
states. The special feature of these solutions is that its current does not
vanish when the quasi-momentum of the state approaches the values equal to the
half of the lattice constant. To explain the bifurcations found in numerical
simulations a simple perturbative approach is developed. The stability of the
nonlinear states is examined by linear spectral analysis and by direct
numerical simulations. An experimental scheme allowing the observation of the
discussed nonlinear current states is suggested and studied by numerical
simulations.
