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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 949–954 (Mi semr1105)  

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

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


DOI: https://doi.org/10.33048/semi.2019.16.063

Full text: PDF file (133 kB)
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Bibliographic databases:

UDC: 517.938
MSC: 35L65,37J35
Received May 18, 2019, published July 1, 2019

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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