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Mathematics of the USSR-Izvestiya, 1991, Volume 37, Issue 2, Pages 397–419
DOI: https://doi.org/10.1070/IM1991v037n02ABEH002069 (Mi im1062) 		 
This article is cited in 260 scientific papers (total in 260 papers)

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

S. P. Tsarev
English version PDF (1183 kB) Citations (260)
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DOI: https://doi.org/10.1070/IM1991v037n02ABEH002069
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.
Received: 18.10.1989
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1990, Volume 54, Issue 5, Pages 1048–1068
Bibliographic databases:
UDC: 514.763.85
MSC: Primary 58F05, 70H05; Secondary 58F07, 58F37, 73B99, 35Q20
Language: English
Original paper language: Russian
Citation: S. P. Tsarev, “The geometry of Hamiltonian 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 Hamiltonian 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/im1062}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1086085}
\zmath{https://zbmath.org/?q=an:0796.76014}
\adsnasa{https://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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  • https://doi.org/10.1070/IM1991v037n02ABEH002069
  • https://www.mathnet.ru/eng/im/v54/i5/p1048
    • This publication is cited in the following 260 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:1468
    Russian version PDF:648
    English version PDF:48
    References:92
    First page:5
     
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