Ev. Ferapontov et Ap. Fordy, SEPARABLE HAMILTONIANS AND INTEGRABLE SYSTEMS OF HYDRODYNAMIC TYPE, Journal of geometry and physics, 21(2), 1997, pp. 169-182
We exhibit a surprising relationship between separable Hamiltonians an
d integrable, linearly degenerate systems of hydrodynamic type. This g
ives a new way of obtaining the general solution of the latter Our for
mulae also lead to interesting canonical transformations between large
classes of Stackel systems.