Commun. Comput. Phys., 2 (2007), pp. 783-794.


Laminated Wave Turbulence: Generic Algorithms II

Elena Kartashova 1*, Alexey Kartashov 2

1 Research Institute for Symbolic Computations, Johannes Kepler University, Altenbergerstr. 69, Linz, A-4040, Austria.
2 AK-Soft, Pillweinstr. 41, Linz, A-4020, Austria.

Received 19 October 2006; Accepted (in revised version) 30 November 2006
Available online 29 January 2007

Abstract

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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PACS: 47.27.E-, 67.40.Vs, 67.57.Fg
Key words: Laminated wave turbulence, discrete wave systems, computations in integers, transcendental algebraic equations, complexity of algorithm.

*Corresponding author.
Email: lena@risc.uni-linz.ac.at (E. Kartashova), alexkart1@gmx.at (A. Kartashov)
 

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