A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems

DOI10.1016/S0034-4877(09)90038-6zbMath1204.37069arXiv0803.0308MaRDI QIDQ963232

Maciej Błaszak, Artur Sergyeyev

Publication date: 8 April 2010

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0308

zbMATH Keywords

conservation lawsRiemann invariantsKilling tensorreciprocal transformationsdispersionless integrable systems\(L\)-tensorgeneralized hodograph methodweakly nonlinear semi-Hamiltonian hydrodynamic-type systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (7)

Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model ⋮ On Reciprocal Equivalence of Stäckel Systems ⋮ The commutative property of reciprocal transformations and dimensional deformations ⋮ Non-homogeneous hydrodynamic systems and quasi-Stäckel Hamiltonians ⋮ Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems ⋮ Miura-reciprocal transformations and localizable Poisson pencils ⋮ Extended symmetry analysis of an isothermal no-slip drift flux model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant integrability criterion for equations of hydrodynamic type
• Hamiltonian formalism of weakly nonlinear hydrodynamic systems
• Bäcklund transformations and their applications
• Separable Hamiltonians and integrable systems of hydrodynamic type
• Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems.
• Dupin hypersurfaces and integrable Hamiltonian systems of hydrodynamic type which do not possess Riemann invariants
• Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems
• Hydrodynamic reductions and solutions of a universal hierarchy
• Invariant solutions of hydrodynamic-type equations
• A class of nonconservative Lagrangian systems on Riemannian manifolds
• From Stäckel systems to integrable hierarchies of PDE’s: Benenti class of separation relations
• Reciprocal transformations and local Hamiltonian structures of hydrodynamic-type systems
• Bäcklund transformations for systems of conservation laws
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Separable systems with quadratic in momenta first integrals
• Towards a Theory of Differential Constraints of a Hydrodynamic Hierarchy
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• 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

This page was built for publication: A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems