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.

arXiv comment24 pages

References in corpus (3)

• Separation of Variables. New Trends.
• Towards a theory of differential constraints of a hydrodynamic hierarchy
• Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems

Cited by in corpus (7)

• Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
• Separability in Riemannian Manifolds
• Natural coordinates for a class of Benenti systems
• Construction of coupled Harry Dym hierarchy and its solutions from Stäckel systems
• On reciprocal equivalence of Stäckel systems
• Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
• Non-Homogeneous Hydrodynamic Systems and Quasi-Stäckel Hamiltonians