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Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface. / Agapov, S. V.; Mironov, A. E.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 327, No. 1, 01.04.2025, p. 1-11.

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

Harvard

Agapov, SV & Mironov, AE 2025, 'Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface', Proceedings of the Steklov Institute of Mathematics, vol. 327, no. 1, pp. 1-11. https://doi.org/10.1134/S0081543824060014

APA

Agapov, S. V., & Mironov, A. E. (2025). Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface. Proceedings of the Steklov Institute of Mathematics, 327(1), 1-11. https://doi.org/10.1134/S0081543824060014

Vancouver

Agapov SV, Mironov AE. Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface. Proceedings of the Steklov Institute of Mathematics. 2025 Apr 1;327(1):1-11. doi: 10.1134/S0081543824060014

Author

Agapov, S. V. ; Mironov, A. E. / Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface. In: Proceedings of the Steklov Institute of Mathematics. 2025 ; Vol. 327, No. 1. pp. 1-11.

BibTeX

@article{164c1db65c804176b475305a7d36f6f7,
title = "Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface",
abstract = "We show that the one-dimensional Schr{\"o}dinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In the case of the Schr{\"o}dinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker–Akhiezer function.",
keywords = "Baker–Akhiezer function, Schr{\"o}dinger equation, finite-gap potential, geodesics, integrability, metrizability",
author = "Agapov, {S. V.} and Mironov, {A. E.}",
note = "This work was supported by the Russian Science Foundation under grant no. 24-11-00281, https://rscf.ru/en/project/24-11-00281/, and performed at Novosibirsk State University. Agapov, S. V. Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface / S. V. Agapov, A. E. Mironov // Proceedings of the Steklov Institute of Mathematics. – 2024. – Vol. 327, No. 1. – P. 1-11. – DOI 10.1134/S0081543824060014. ",
year = "2025",
month = apr,
day = "1",
doi = "10.1134/S0081543824060014",
language = "English",
volume = "327",
pages = "1--11",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "ФГБУ {"}Издательство {"}Наука{"}",
number = "1",

}

RIS

TY - JOUR

T1 - Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface

AU - Agapov, S. V.

AU - Mironov, A. E.

N1 - This work was supported by the Russian Science Foundation under grant no. 24-11-00281, https://rscf.ru/en/project/24-11-00281/, and performed at Novosibirsk State University. Agapov, S. V. Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface / S. V. Agapov, A. E. Mironov // Proceedings of the Steklov Institute of Mathematics. – 2024. – Vol. 327, No. 1. – P. 1-11. – DOI 10.1134/S0081543824060014.

PY - 2025/4/1

Y1 - 2025/4/1

N2 - We show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In the case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker–Akhiezer function.

AB - We show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In the case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker–Akhiezer function.

KW - Baker–Akhiezer function

KW - Schrödinger equation

KW - finite-gap potential

KW - geodesics

KW - integrability

KW - metrizability

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UR - https://elibrary.ru/item.asp?id=80615963

U2 - 10.1134/S0081543824060014

DO - 10.1134/S0081543824060014

M3 - Article

VL - 327

SP - 1

EP - 11

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 65163360