Wave-vector resonance in a nonlinear multiwavespeed chaotic billiard

Nonlinear coupling between eigenmodes of a system leads to spectral energy redistribution. For multiwavespeed chaotic billiards, the average coupling strength can exhibit sharp discontinuities as a function of frequency related to wave-vector coincidences between constituent waves of different wavespeeds. The phenomenon is investigated numerically for an ensemble of two-dimensional square two-wavespeed billiards with rough boundaries and quadratic nonlinearity representative of elastodynamic waves. Results of direct numerical simulations are compared with theoretical predictions.