Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions
E.V. Ferapontov, A. Moro, V.V. Sokolov
TL;DR
This paper classifies multi-dimensional Hamiltonian systems of hydrodynamic type, providing a complete list of integrable cases with dispersionless Lax pairs and hydrodynamic reductions, advancing understanding of their structure.
Contribution
It offers a comprehensive classification of 2- and 3-component integrable Hamiltonian systems in 2+1 dimensions with explicit examples.
Findings
Complete list of integrable Hamiltonians obtained
All examples have dispersionless Lax pairs
Infinite hydrodynamic reductions identified
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.
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