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

Gulshat Abdikalikova; Andrey Evgenevich Mironov

doi:10.33048/semi.2019.16.063

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

Gulshat Abdikalikova, Andrey Evgenevich Mironov

Research output: Contribution to journal › Article › peer-review

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.

Translated title of the contribution	О точных решениях системы квазилинейных уравнений, описывающей интегрируемые геодезические потоки на поверхности
Original language	English
Pages (from-to)	949-954
Number of pages	6
Journal	Сибирские электронные математические известия
Volume	16
DOIs	https://doi.org/10.33048/semi.2019.16.063
Publication status	Published - 1 Jan 2019

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1.01 MATHEMATICS

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38 GEOLOGY

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10.33048/semi.2019.16.063

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

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",

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KW - The generalized hodograph method

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

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