  We study the properties of mode-mode interactions for waves propagating in
nonlinear disordered one-dimensional systems. We focus on i) the localization
volume of a mode which defines the number of interacting partner modes, ii) the
overlap integrals which determine the interaction strength, iii) the average
spacing between eigenvalues of interacting modes, which sets a scale for the
nonlinearity strength, and iv) resonance probabilities of interacting modes.
Our results are discussed in the light of recent studies on spreading of wave
packets in disordered nonlinear systems, and are related to the quantum many
body problem in a random chain.
