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The geometry of Hamiltonian systems of hydrodynamic type. The generalized hodograph method. (English. Russian original) Zbl 0796.76014
Math. USSR, Izv. 37, No. 2, 397-419 (1991); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 5, 1048-1068 (1990).
Summary: 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.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
35Q35 PDEs in connection with fluid mechanics
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