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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 326, Pages 330–367
DOI: https://doi.org/10.4213/tm4423 (Mi tm4423) 		 
On the Monodromy-Preserving Deformation of a Double Confluent Heun Equation

S. I. Tertichniy

Russian Metrological Institute of Technical Physics and Radioengineering, Mendeleyevo, Moscow oblast, Russia
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DOI: https://doi.org/10.4213/tm4423
Abstract: We consider the second-order linear differential equation presented in Subsection 4.8 of the paper by J. Dereziński, A. Ishkhanyan, and A. Latosiński [SIGMA 17, 056 (2021)] and called there the deformed double confluent Heun equation. We prove that the additional singular point arising during the construction of the equation does not affect the analytic structure of its solution space. Moreover, we prove that under certain conditions a one-parameter transformation of the equation, called a deformation, with coefficients expressed in terms of the third Painlevé transcendent, leaves its monodromy unchanged. The proofs are self-contained.
Keywords: double confluent Heun equation, deformed double confluent Heun equation, nondestructive singular point, Frobenius norm, third Painlevé transcendent, transport equation, isomonodromicity
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: January 3, 2024
Revised: May 24, 2024
Accepted: June 21, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 326, Pages 303–338
DOI: https://doi.org/10.1134/S0081543824040151
Document Type: Article
UDC: 517.926.4
Language: Russian
Citation: S. I. Tertichniy, “On the Monodromy-Preserving Deformation of a Double Confluent Heun Equation”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 330–367; Proc. Steklov Inst. Math., 326 (2024), 303–338
Citation in format AMSBIB
\Bibitem{Ter24}
\by S.~I.~Tertichniy
\paper On the Monodromy-Preserving Deformation of a Double Confluent Heun Equation
\inbook Topology, Geometry, Combinatorics, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 326
\pages 330--367
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4423}
\crossref{https://doi.org/10.4213/tm4423}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 326
\pages 303--338
\crossref{https://doi.org/10.1134/S0081543824040151}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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