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Journal of Dynamical and Control Systems
Erschienen in: Journal of Dynamical and Control Systems 1/2022

27.08.2021

Stokes Matrices of a Reducible Double Confluent Heun Equation via Monodromy Matrices of a Reducible General Huen Equation with Symmetric Finite Singularities

verfasst von: Tsvetana Stoyanova

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 1/2022

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Abstract

We study the effect of the unfolding of a reducible double confluent Heun equation from the point of view of the Stokes phenomenon. We introduce a small complex parameter ε that splits together the non-resonant singular points x = 0 and \(x=\infty \) into four different Fuchsian singularities \(x_{L}=-\sqrt {\varepsilon }, x_{R}=\sqrt {\varepsilon }\), and \(x_{LL}=-1/\sqrt {\varepsilon }, x_{RR}=1/\sqrt {\varepsilon }\), respectively. The perturbed equation is a symmetric general Heun equation and its general solution depends analytically on \(\sqrt {\varepsilon }\). Then we prove that when the perturbed equation has exactly two resonant singularities of different type, all the Stokes matrices of the initial double confluent Heun equation are realized as a limit of the upper-triangular parts of the monodromy matrices of the perturbed equation when \(\sqrt {\varepsilon } \rightarrow 0\). To establish this result we combine a direct computation with a theoretical approach.
Vorheriger Artikel Global Large Solutions to the Cauchy Problem of Planar Magnetohydrodynamics Equations with Temperature-Dependent Coefficients
Nächster Artikel Correction to : Stokes Matrices of a Reducible Double Confluent Heun Equation via Monodromy Matrices of a Reducible General Huen Equation with Symmetric Finite Singularities

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Metadaten
Titel
Stokes Matrices of a Reducible Double Confluent Heun Equation via Monodromy Matrices of a Reducible General Huen Equation with Symmetric Finite Singularities
verfasst von
Tsvetana Stoyanova
Publikationsdatum
27.08.2021
Verlag
Springer US
Erschienen in
Journal of Dynamical and Control Systems / Ausgabe 1/2022
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-021-09571-0

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