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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 949–954
DOI: https://doi.org/10.33048/semi.2019.16.063 (Mi semr1105) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Differentical equations, dynamical systems and optimal control

On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface

G. Abdikalikovaa, A. E. Mironovba

a Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
b Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2019.16.063
Abstract: In this paper, for the first time, explicit solutions of a semi-Hamiltonian system of quasi-linear differential equations by the generalized hodograph method are found. These solutions define (local) metrics on a surface for which the geodesic flow has a polynomial in momenta integrals of the fourth degree.
Keywords: integrable geodesic flows, the generalized hodograph method.
Funding agency Grant number
Russian Science Foundation 19-11-00044
Received May 18, 2019, published July 1, 2019
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 35L65,37J35
Language: Russian
Citation: G. Abdikalikova, A. E. Mironov, “On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface”, Sib. Èlektron. Mat. Izv., 16 (2019), 949–954
Citation in format AMSBIB
\Bibitem{AbdMir19}
\by G.~Abdikalikova, A.~E.~Mironov
\paper On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 949--954
\mathnet{http://mi.mathnet.ru/semr1105}
\crossref{https://doi.org/10.33048/semi.2019.16.063}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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