Stationary systems of the AKNS hierarchy

TL;DR

This paper demonstrates that stationary systems within the AKNS hierarchy are classical separable Stäckel systems, providing explicit transformations between jet variables and separation coordinates through Lax representations.

Contribution

It establishes a connection between stationary AKNS systems and classical separable Stäckel systems, with explicit coordinate transformation methods.

Findings

Stationary AKNS systems are classical separable Stäckel systems.

Explicit transformation from jet variables to separation coordinates is derived.

Lax representations are used to compare jet and separable coordinates.

Abstract

In this article we investigate stationary systems of the AKNS hierarchy. We prove that all these systems are classical separable St\"ackel systems. The explicit transformation from jet variables to separation coordinates is obtained by comparing Lax representations in jet and separable coordinates.