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

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

#### 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

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