Fast computation algorithm for discrete resonances among gravity waves

Traditionally resonant interactions among short waves with large real wave-numbers were described statistically, and only a small domain in the spectral space with integer wave-numbers, i.e. discrete resonances, had to be studied separately in resonators. Numerical simulations of the last few years have shown unambiguously the existence of some discrete effects in the short-wave part of the wave spectrum. Newly presented model of laminated turbulence explains theoretically the appearance of these effects, thus putting forth a novel problem-construction of fast algorithms for computation of solutions of resonance conditions with integer wave-numbers of orders 10(3) and more. Example of such an algorithm for 4-wave interactions of gravity waves is given. Its generalization for different types of waves is briefly discussed.