Recursion Operators for Rational Bundle on $\mathfrak{sl}(3,\mathbb{C})$ with $\mathbb{Z}_2\times \mathbb{Z}_2\times \mathbb{Z}_2$ Reduction of Mikhailov Type

Abstract

We consider the recursion operator related to a system introduced recently that could be considered as a generalization to a pole gauge generalized Zakharov-Shabat system on $\mathfrak{sl}(3,\mathbb{C})$ but involving rational dependence on the spectral parameter and subject to $\mathbb{Z}_2\times \mathbb{Z}_2\times \mathbb{Z}_2$ reduction of Mikhailov type. We calculate the hierarchies of nonlinear evolution equations related to this system through the recursion operators we introduce.