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.
| Original language | English |
|---|---|
| Pages (from-to) | 783-794 |
| Number of pages | 12 |
| Journal | Communications in Computational Physics |
| Volume | 2 |
| Issue number | 4 |
| Publication status | Published - Aug 2007 |
Fields of science
- 101 Mathematics
- 101001 Algebra
- 101005 Computer algebra
- 101009 Geometry
- 101012 Combinatorics
- 101013 Mathematical logic
- 101020 Technical mathematics