Laminated Wave Turbulence: Generic Algorithms II (Communications in Computational Physics, 2007)
The model of laminated wave turbulence puts forth a novel computationalproblem–construction of fast algorithms for finding exact solutions of Diophantineequations in integers of order 1012 and more. The equations to be solved in integers areresonant conditions for nonlinearly interacting waves and their form is defined by thewave dispersion. It is established that for the most common dispersion as an arbitraryfunction of a wave-vector length two different generic algorithms are necessary: (1)one-class-case algorithm for waves interacting through scales, and (2) two-class-casealgorithm for waves interacting through phases. In our previous paper we describedthe one-class-case generic algorithm and in our present paper we present the two-class-case generic algorithm.