On Generalized WKB Expansion of Monodromy Generating Function

We study symplectic properties of the monodromy map of the Schrödinger equation on a Riemann surface with a meromorphic potential having second-order poles. At first, we discuss the conditions for the base projective connection, which induces its own set of Darboux homological coordinates, to imply...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2023
1. Verfasser: Klimov, Roman
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2023
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211917
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On Generalized WKB Expansion of Monodromy Generating Function. Roman Klimov. SIGMA 19 (2023), 026, 36 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Klimov, Roman
author_facet Klimov, Roman
citation_txt On Generalized WKB Expansion of Monodromy Generating Function. Roman Klimov. SIGMA 19 (2023), 026, 36 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We study symplectic properties of the monodromy map of the Schrödinger equation on a Riemann surface with a meromorphic potential having second-order poles. At first, we discuss the conditions for the base projective connection, which induces its own set of Darboux homological coordinates, to imply the Goldman Poisson structure on the character variety. Using this result, we extend the paper [Theoret. and Math. Phys. 206 (2021), 258-295, arXiv:1910.07140], by performing a generalized WKB expansion of the generating function of monodromy symplectomorphism (the Yang-Yang function) and computing its first three terms.
first_indexed 2026-03-17T18:24:05Z
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language English
last_indexed 2026-03-17T18:24:05Z
publishDate 2023
publisher Інститут математики НАН України
record_format dspace
spelling Klimov, Roman
2026-01-16T11:19:04Z
2023
On Generalized WKB Expansion of Monodromy Generating Function. Roman Klimov. SIGMA 19 (2023), 026, 36 pages
1815-0659
2020 Mathematics Subject Classification: 53D30; 34M45; 34E20
arXiv:2206.10578
https://nasplib.isofts.kiev.ua/handle/123456789/211917
https://doi.org/10.3842/SIGMA.2023.026
We study symplectic properties of the monodromy map of the Schrödinger equation on a Riemann surface with a meromorphic potential having second-order poles. At first, we discuss the conditions for the base projective connection, which induces its own set of Darboux homological coordinates, to imply the Goldman Poisson structure on the character variety. Using this result, we extend the paper [Theoret. and Math. Phys. 206 (2021), 258-295, arXiv:1910.07140], by performing a generalized WKB expansion of the generating function of monodromy symplectomorphism (the Yang-Yang function) and computing its first three terms.
The author thanks his scientific advisor, D. Korotkin, for posing the problem and for fruitful discussions, and is grateful to anonymous referees for carefully reading the manuscript and making a relevant contribution to enhance the paper.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Generalized WKB Expansion of Monodromy Generating Function
Article
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spellingShingle On Generalized WKB Expansion of Monodromy Generating Function
Klimov, Roman
title On Generalized WKB Expansion of Monodromy Generating Function
title_full On Generalized WKB Expansion of Monodromy Generating Function
title_fullStr On Generalized WKB Expansion of Monodromy Generating Function
title_full_unstemmed On Generalized WKB Expansion of Monodromy Generating Function
title_short On Generalized WKB Expansion of Monodromy Generating Function
title_sort on generalized wkb expansion of monodromy generating function
url https://nasplib.isofts.kiev.ua/handle/123456789/211917
work_keys_str_mv AT klimovroman ongeneralizedwkbexpansionofmonodromygeneratingfunction