## Proceedings of the International Conference on Geometry, Integrability and Quantization

- Geom. Integrability & Quantization
- 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

### $N$-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

**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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