Separable Hamiltonians and integrable systems of hydrodynamic type. (English) Zbl 0865.58018
Summary: We exhibit a surprising relationship between separable Hamiltonians and integrable, linearly degenerate systems of hydrodynamic type. This gives a new way of obtaining the general solution of the latter. Our formulae also lead to interesting canonical transformations between large classes of Stäckel systems.
MSC:
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
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