ON PROPERTIES OF WEAKLY NONLINEAR-WAVE INTERACTIONS IN RESONATORS

Weakly nonlinear wave interactions in resonators are considered. Qualitative differences from the continuous case are found: prevalence of waves not taking part in any interactions at all; dependence of the number of interacting waves on the basin form; existence of basins where interactions are totally impossible; locality of interactions in the spectral space. Consideration of equations defining the resonance surface in finite fields as well as methods of number theory are used. Some aspects of relations between the continuous and discrete cases are discussed.