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.
Communications in Mathematical Physics
- Pub Date:
- January 2009
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- Mathematics - Differential Geometry
- 34 pages