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VOL. 2 | 2001 On the Reductions and Hamiltonian Structures of N-Wave Type Equations
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 $\mathbb{Z}_2$ and $\mathbb{Z}_2 \times \mathbb{Z}_2$-reductions including ones that can be embedded also in the Weyl group of $\mathfrak{g}$. The consequences of these restrictions on the properties of their Hamiltonian structures are analyzed on specific examples which find applications to nonlinear optics.

Information

Published: 1 January 2001
First available in Project Euclid: 5 June 2015

zbMATH: 1072.37050
MathSciNet: MR1815637

Digital Object Identifier: 10.7546/giq-2-2001-156-170

Rights: Copyright © 2001 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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