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
Date:2023
Main Author: Klimov, Roman
Format: Article
Language:English
Published: Інститут математики НАН України 2023
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
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Summary: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.
ISSN:1815-0659