Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems

Abstract

A systematic construction of Stäckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One Casimir bi-Hamiltonian case is studed in details and in this case, a systematic construction of related hydrodynamic systems in arbitrary coordinates is presented, using a cofactor method and soliton symmetry constraints.

to appear in Journal of Geometry and Physics

References in corpus (2)

• Separation of variables in quasi-potential systems of bi-cofactor form
• Binary Constrained Flows and Separation of Variables for Soliton Equations

Cited by in corpus (9)

• Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems
• Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
• Separability in Riemannian Manifolds
• From Stäckel systems to integrable hierarchies of PDE's: Benenti class of separation relations
• Hydrodynamic Reductions of Dispersionless Harry Dym Hierarchy
• Non-Hamiltonian systems separable by Hamilton-Jacobi method
• Reciprocal transformations for Stackel-related Liouville integrable systems
• Systematic construction of separable systems with quadratic in momenta first integrals
• Integrable multi-phase thermodynamic systems and Tsallis' composition rule