Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type

Abstract

We study purely nonlocal Hamiltonian structures for systems of hydrodynamic type. In the case of a semi-Hamiltonian system, we show that such structures are related to quadratic expansions of the diagonal metrics naturally associated with the system.

arXiv comment23pp

References in corpus (4)

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Hamiltonian structure of reductions of the Benney system
• Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies and the equations of associativity
• New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems

Cited by in corpus (2)

• $F$-manifolds and integrable systems of hydrodynamic type
• Reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures