  We develop the theory of nonlinear localised modes (intrinsic localised modes
or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We
consider different geometries of the waveguides created by an array of
nonlinear dielectric rods in an otherwise perfect linear 2D photonic crystal,
and demonstrate that the effective interaction in such waveguides is nonlocal,
being described by a new type of nonlinear lattice models with long-range
coupling and nonlocal nonlinearity. We reveal the existence of different types
of nonlinear guided modes which are also localised in the waveguide direction,
and describe their unique properties including bistability.
