From Stäckel systems to integrable hierarchies of PDE's: Benenti class of separation relations

Abstract

We propose a general scheme of constructing of soliton hierarchies from finite dimensional Stäckel systems and related separation relations. In particular, we concentrate on the simplest class of separation relations, called Benenti class, i.e. certain Stäckel systems with quadratic in momenta integrals of motion.

24 pages