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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211917 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862688817350180864 |
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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.
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| first_indexed | 2026-03-17T18:24:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211917 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Generalized WKB Expansion of Monodromy Generating Function Article published earlier |
| 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 |