Some Aspects of the Spectral Theory for \(\frak{sl}(3,\mathbb{C})\) System with \(\mathbb{Z}_2 ×\mathbb{Z}_2× \mathbb{Z}_2\) Reduction of Mikhailov Type with General Posititon Boundary Conditions

Abstract

We consider some aspects of the spectral theory of a system that is a generalization to a pole gauge Zakharov-Shabat type system on the Lie algebra $\frak{sl}(3,\mathbb{C})$ but involving rational dependence on the spectral parameter and subjected to $\mathbb{Z}_2\times \mathbb{Z}_2\times \mathbb{Z}_2$ reduction of Mikhailov type. The question of the existence of analytic fundamental solutions under some special type of boundary conditions has been considered, recently we consider boundary conditions in general position.