From St\"{a}ckel 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 St\"{a}ckel systems and related separation relations. In particular, we concentrate on the simplest class of separation relations, called Benenti class, i.e. certain St\"{a}ckel systems with quadratic in momenta integrals of motion.Comment: 24 page