  We introduce a new coupled mode theory to model nonlinear Schr\"odinger
equations for contra- propagating Bloch modes that include disorder-induced
multiple scattering effects on nonlinear soliton propagation in photonic
crystal waveguides. We also derive sub unit-cell coupling coefficients and use
these to introduce a generalized length scale associated with each coupling
effect. In particular, we define a multiple-scattering length scale that
quantifies the spatial extent of a disorder- induced cavity mode. Our numerical
simulations of nonlinear pulse propagation are in excellent qualitative
agreement with recent experiments and provide insight into how disorder
inhibits soliton propagation and other nonlinear propagation effects in
photonic crystal waveguides.
