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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 5, Pages 991–1006 (Mi izv978)  

This article is cited in 2 scientific papers (total in 2 papers)

Breaking solitons. VI. Extension of systems of hydrodynamic type

O. I. Bogoyavlenskii


Abstract: Systems of differential equations, admitting the Lax representation and extending the systems of hydrodynamic type, connected with the Volterra model and Toda lattice, are presented. A construction of differential operator equations with derivatives of arbitrary order with respect to the variables $t$ and $y$ and possessing a reduction preserving the eigenvalues of the corresponding operator $L$ is suggested. Dynamical systems having a Lax representation and generalizing the Toda lattice are constructed. A construction of integrable Euler equations admitting a Lax representation with $n$ independent spectral parameters and connected with $n$ Riemann surfaces is found.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:2, 959–973

Bibliographic databases:

UDC: 517.91
MSC: 35Q51, 76B25
Received: 06.05.1991

Citation: O. I. Bogoyavlenskii, “Breaking solitons. VI. Extension of systems of hydrodynamic type”, Izv. Akad. Nauk SSSR Ser. Mat., 55:5 (1991), 991–1006; Math. USSR-Izv., 39:2 (1992), 959–973

Citation in format AMSBIB
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\by O.~I.~Bogoyavlenskii
\paper Breaking solitons. VI.~Extension of systems of hydrodynamic type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 5
\pages 991--1006
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\zmath{https://zbmath.org/?q=an:0789.35141}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..39..959B}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 2
\pages 959--973
\crossref{https://doi.org/10.1070/IM1992v039n02ABEH002233}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JZ92300002}


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    This publication is cited in the following articles:
    1. Zhenyun Qin, Ruguang Zhou, “A (2+1)-dimensional breaking soliton equation associated with the Kaup–Newell soliton hierarchy”, Chaos, Solitons & Fractals, 21:2 (2004), 311  crossref
    2. Zhao Song-Lin, Zhang Da-Jun, Ji Jie, “Exact Solutions for Two Equation Hierarchies”, Chinese Phys Lett, 27:2 (2010), 020201  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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