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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 327, Pages 7–17
DOI: https://doi.org/10.4213/tm4435 (Mi tm4435) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

S. V. Agapovab, A. E. Mironovab

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Full-text PDF (295 kB) Citations (1) English version article
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DOI: https://doi.org/10.4213/tm4435
Abstract: 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.
Keywords: Schrödinger equation, finite-gap potential, Baker–Akhiezer function, metrizability, geodesics, integrability.
Funding agency Grant number
Russian Science Foundation 24-11-00281
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.
Received: June 6, 2024
Revised: July 1, 2024
Accepted: August 13, 2024
Published: 12.03.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 327, Pages 1–11
DOI: https://doi.org/10.1134/S0081543824060014
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. V. Agapov, A. E. Mironov, “Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 7–17; Proc. Steklov Inst. Math., 327 (2024), 1–11
Citation in format AMSBIB
\Bibitem{AgaMir24}
\by S.~V.~Agapov, A.~E.~Mironov
\paper Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 7--17
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4435}
\crossref{https://doi.org/10.4213/tm4435}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 1--11
\crossref{https://doi.org/10.1134/S0081543824060014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001525773}
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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