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VOL. 20 | 2019 Hierarchies of Symplectic Structures for $\mathfrak{sl}(3,\mathbb{C})$ Zakharov-Shabat Systems in Canonical and Pole Gauge with $\mathbb{Z}_2\times \mathbb{Z}_2$ Reduction of Mikhailov Type
Alexandar Yanovski

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

We consider the theory of the hierarchies of nonlinear evolution equations associated with two gauge-equivalent auxiliary systems. They are obtained from the Generalized Zakharov-Shabat system on $\mathfrak{sl}(3,\mathbb{C})$ in general position making a $\mathbb{Z}_2\times \mathbb{Z}_2$ reductions of Mikhailov type in canonical and in pole gauge respectively. Using the Recursion Operators approach we study the symplectic structures of the hierarchies of the nonlinear evolution equations associated with the above auxiliary systems and find the relation between them.

Information

Published: 1 January 2019
First available in Project Euclid: 21 December 2018

zbMATH: 1417.35158
MathSciNet: MR3887759

Digital Object Identifier: 10.7546/giq-20-2019-297-310

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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