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

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.