Standard

Integrable magnetic geodesic flows on 2-surfaces. / Agapov, Sergei; Potashnikov, Alexey; Shubin, Vladislav.

In: Nonlinearity, Vol. 36, No. 4, 2128, 01.04.2023.

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

Harvard

Agapov, S, Potashnikov, A & Shubin, V 2023, 'Integrable magnetic geodesic flows on 2-surfaces', Nonlinearity, vol. 36, no. 4, 2128. https://doi.org/10.1088/1361-6544/acc0c5

APA

Agapov, S., Potashnikov, A., & Shubin, V. (2023). Integrable magnetic geodesic flows on 2-surfaces. Nonlinearity, 36(4), [2128]. https://doi.org/10.1088/1361-6544/acc0c5

Vancouver

Agapov S, Potashnikov A, Shubin V. Integrable magnetic geodesic flows on 2-surfaces. Nonlinearity. 2023 Apr 1;36(4):2128. doi: 10.1088/1361-6544/acc0c5

Author

Agapov, Sergei ; Potashnikov, Alexey ; Shubin, Vladislav. / Integrable magnetic geodesic flows on 2-surfaces. In: Nonlinearity. 2023 ; Vol. 36, No. 4.

BibTeX

@article{d8b50aeb38044c0088038898b5b3e97b,
title = "Integrable magnetic geodesic flows on 2-surfaces",
abstract = "We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of partial differential equations (PDEs) appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.",
keywords = "33C05, 35C05, 37J35, 53D25, 70H06, Legendre transformation, Riemann invariants, first integral, generalized hodograph method, hypergeometric functions, magnetic geodesic flow, semi-Hamiltonian system",
author = "Sergei Agapov and Alexey Potashnikov and Vladislav Shubin",
note = "S. Agapov and V. Shubin are supported by the Mathematical Center in Akademgorodok under the Agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.",
year = "2023",
month = apr,
day = "1",
doi = "10.1088/1361-6544/acc0c5",
language = "English",
volume = "36",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - Integrable magnetic geodesic flows on 2-surfaces

AU - Agapov, Sergei

AU - Potashnikov, Alexey

AU - Shubin, Vladislav

N1 - S. Agapov and V. Shubin are supported by the Mathematical Center in Akademgorodok under the Agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of partial differential equations (PDEs) appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.

AB - We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of partial differential equations (PDEs) appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.

KW - 33C05

KW - 35C05

KW - 37J35

KW - 53D25

KW - 70H06

KW - Legendre transformation

KW - Riemann invariants

KW - first integral

KW - generalized hodograph method

KW - hypergeometric functions

KW - magnetic geodesic flow

KW - semi-Hamiltonian system

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85150530616&origin=inward&txGid=522af83f61f1b699e0ddfd952a3a4444

UR - https://www.mendeley.com/catalogue/5e504400-bccb-324d-9292-660fe00caefe/

U2 - 10.1088/1361-6544/acc0c5

DO - 10.1088/1361-6544/acc0c5

M3 - Article

VL - 36

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 4

M1 - 2128

ER -

ID: 59245240