Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions
arXiv:0710.2012 · doi:10.1007/s00220-008-0522-5
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