The geometry of Hamiltonian systems of hydrodynamic type. The generalized hodograph method

S. P. Tsarev

Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 397-419.

Résumé

It is proved that there exists an infinite involutive family of integrals of hydrodynamic type for diagonal Hamiltonian systems of quasilinear equations; the completeness of the family is also proved, and a basis for it is constructed for Whitham's equation. Higher integrals and symmetries of these systems are found.

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