Stationary Systems of the AKNS Hierarchy

Abstract We investigate what we call stationary systems of the AKNS hierarchy, that is finite dimensional systems consisting of a stationary flow of the AKNS hierarchy and of all the lower flows of the hierarchy. We prove that all these systems are in fact classical separable Stäckel systems. We also present an explicit transformation from jet variables to separation coordinates that turns a stationary AKNS system into a corresponding Stäckel system. This transformation is obtained by comparing Lax representations of considered systems in jet and in separable coordinates.