Tsarëv, S. P. 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. Cited in 3 ReviewsCited in 143 Documents 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 Keywords:averaged completely integrable equations; Benney’s equations; infinite involutive family of integrals; diagonal Hamiltonian systems of quasilinear equations; Whitham’s equation; symmetries PDFBibTeX XMLCite \textit{S. P. Tsarëv}, Math. USSR, Izv. 37, No. 2, 397--419 (1990; Zbl 0796.76014); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 5, 1048--1068 (1990) Full Text: DOI