Geodesic
On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 949-954.

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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. 
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G. Abdikalikova; A. E. Mironov. On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 949-954. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a92/

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