## 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

Dates
First available in Project Euclid: 13 July 2015

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