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VOL. 3 | 2002 $N$-Wave Type Systems and their Gauge Equivalent Related to the Orthogonal Algebras
Vladimir Gerdjikov, Georgi Grahovski, Nikolay Kostov

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber

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.

Information

Published: 1 January 2002
First available in Project Euclid: 12 June 2015

zbMATH: 1219.37051
MathSciNet: MR1884850

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