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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 5, Pages 1048–1068 (Mi izv1062)  

This article is cited in 155 scientific papers (total in 155 papers)

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

S. P. Tsarev


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1991, 37:2, 397–419

Bibliographic databases:

UDC: 514.763.85
MSC: Primary 58F05, 70H05; Secondary 58F07, 58F37, 73B99, 35Q20
Received: 18.10.1989

Citation: S. P. Tsarev, “The geometry of harniltonian systems of hydrodynamic type. The generalized hodograph method”, Izv. Akad. Nauk SSSR Ser. Mat., 54:5 (1990), 1048–1068; Math. USSR-Izv., 37:2 (1991), 397–419

Citation in format AMSBIB
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\by S.~P.~Tsarev
\paper The geometry of harniltonian systems of hydrodynamic type. The generalized hodograph method
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 5
\pages 1048--1068
\mathnet{http://mi.mathnet.ru/izv1062}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1086085}
\zmath{https://zbmath.org/?q=an:0796.76014}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..37..397T}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 37
\issue 2
\pages 397--419
\crossref{https://doi.org/10.1070/IM1991v037n02ABEH002069}


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    This publication is cited in the following articles:
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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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