Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

Abstract

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless Lax pairs and an infinity of hydrodynamic reductions.

34 pages

References in corpus (4)

• On integrability of (2+1)-dimensional quasilinear systems
• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
• On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

Cited by in corpus (11)

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• Recursion operators for dispersionless integrable systems in any dimension
• Hamiltonian operators of Dubrovin-Novikov type in 2D
• Shock formation in the dispersionless Kadomtsev-Petviashvili equation
• Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions
• Integrable (3+1)-dimensional system with an algebraic Lax pair
• Classification of degenerate non-homogeneous Hamiltonian operators
• Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions
• Integrable (3+1)-dimensional generalization for dispersionless Davey--Stewartson system