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

OECD FOS+WOS

1.01 MATHEMATICS

State classification of scientific and technological information

38 GEOLOGY

Access to Document

10.33048/semi.2019.16.063

Fingerprint Dive into the research topics of 'On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface'. Together they form a unique fingerprint.

Cite this

@article{f52e8c72437c4f1b8bbb9b3792fffe5a,

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",

author = "Gulshat Abdikalikova and Mironov, {Andrey Evgenevich}",

year = "2019",

month = jan,

day = "1",

doi = "10.33048/semi.2019.16.063",

language = "English",

volume = "16",

pages = "949--954",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

}

TY - JOUR

T1 - On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface

AU - Abdikalikova, Gulshat

AU - Mironov, Andrey Evgenevich

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Integrable geodesic flows

KW - The generalized hodograph method

UR - http://www.scopus.com/inward/record.url?scp=85071187618&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=42735107

U2 - 10.33048/semi.2019.16.063

DO - 10.33048/semi.2019.16.063

M3 - Article

AN - SCOPUS:85071187618

VL - 16

SP - 949

EP - 954

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -