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Volume 2, Issue 4
Laminated Wave Turbulence: Generic Algorithms II

E. Kartashova & A. Kartashov

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

Published online: 2007-02

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  • 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 1012 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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@Article{CiCP-2-783, author = {E. Kartashova and A. Kartashov}, title = {Laminated Wave Turbulence: Generic Algorithms II}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {4}, pages = {783--794}, 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 1012 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7927.html} }
TY - JOUR T1 - Laminated Wave Turbulence: Generic Algorithms II AU - E. Kartashova & A. Kartashov JO - Communications in Computational Physics VL - 4 SP - 783 EP - 794 PY - 2007 DA - 2007/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7927.html KW - AB -

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 1012 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.

E. Kartashova and A. Kartashov. (2007). Laminated Wave Turbulence: Generic Algorithms II. Communications in Computational Physics. 2 (4). 783-794. doi:
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