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Reciprocal transformations and local Hamiltonian structures of hydrodynamic type systems

By Simonetta Abenda


We start from an integrable DN hydrodynamic type system and we settle the necessary conditions on the conservation laws in the reciprocal transformation so that, after such a transformation of the independent variables, one of the metrics associated to the initial system be flat. As a result the conservation laws in the reciprocal transformations have to be linear combinations of the Casimirs, the momentum and the Hamiltonian densities associated to the Hamiltonian operator for the initial metric. Then, we restrict ourselves to the case in which the initial metric is either flat or constant curvature and we classify the reciprocal transformations of one or both the independent variables so that the reciprocal metric is flat. Finally we apply our conditions to some examples.

Year: 2009
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