Proceedings of the International Conference on Geometry, Integrability and Quantization

$N$-Wave Type Systems and their Gauge Equivalent Related to the Orthogonal Algebras

Vladimir Gerdjikov, Georgi Grahovski, and Nikolay Kostov

Abstract

The reductions of the integrable $N$-wave type equations solvable by the inverse scattering method with the generalized Zakharov–Shabat system $L$ and related to some simple Lie algebra $\mathfrak{g}$ are analyzed. Special attention is paid to the $\mathbb{Z}_2$-reductions including ones that can be embedded also in the Weyl group of $\mathfrak{g}$. The consequences of these restrictions on the structure of the dresing factors are outlined. An example of 4-wave equations (with application to nonlinear optics) and its gauge equivalent are given.

Article information

Source
Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2002), 249-261

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1434145472

Digital Object Identifier
doi:10.7546/giq-3-2002-249-261

Mathematical Reviews number (MathSciNet)
MR1884850

Zentralblatt MATH identifier
1219.37051

Citation

Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay. $N$-Wave Type Systems and their Gauge Equivalent Related to the Orthogonal Algebras. Proceedings of the Third International Conference on Geometry, Integrability and Quantization, 249--261, Coral Press Scientific Publishing, Sofia, Bulgaria, 2002. doi:10.7546/giq-3-2002-249-261. https://projecteuclid.org/euclid.pgiq/1434145472


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