Laminated Wave Turbulence: Generic Algorithms II

Details Laminated Wave Turbulence: Generic Algorithms II Laminated Wave Turbulence: Generic Algorithms II

2006-11-17

arxiv.org/abs/math-ph/0611042v1

CiCP (Communications in Computational Physics) 2(4), pp. 783-794.(2007).

Physics

Mathematical Physics

to appear in J. "Communications in Computational Physics" (2006)

Scientific paper

10.1142/S0129183106010042

The model of laminated wave turbulence puts forth a novel computational problem - construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order $10^{12}$ and more. The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion. It is established that for the most common dispersion as an arbitrary function 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-case algorithm for waves interacting through phases. In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-class-case generic algorithm.

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