Proceedings of the International Conference on Geometry, Integrability and Quantization

Poisson-Nijenhuis Structure for Generalized Zakharov-Shabat System in Pole Gauge on the Lie Algebra $\mathfrak{sl}(3,\mathbb{C})$

Alexander B. Yanovski

Abstract

We consider the recursion operator approach to the soliton equations related to a $\mathfrak{sl}(3,\mathbb{C})$ generalized Zakharov-Shabat auxiliary linear system in pole gauge and show that the recursion operator can be identified with the dual to a Nijenhuis tensor for a Poisson-Nijenhuis structure on the manifold of potentials.

Article information

Source
Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2011), 342-353

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815632

Digital Object Identifier
doi:10.7546/giq-12-2011-342-353

Mathematical Reviews number (MathSciNet)
MR3087989

Zentralblatt MATH identifier
1382.53024

Citation

Yanovski, Alexander B. Poisson-Nijenhuis Structure for Generalized Zakharov-Shabat System in Pole Gauge on the Lie Algebra $\mathfrak{sl}(3,\mathbb{C})$. Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization, 342--353, Avangard Prima, Sofia, Bulgaria, 2011. doi:10.7546/giq-12-2011-342-353. https://projecteuclid.org/euclid.pgiq/1436815632


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