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This article is cited in 23 scientific papers (total in 23 papers)
Euler integral symmetries for a deformed Heun equation and symmetries
of the Painlevé PVI equation
A. Ya. Kazakova, S. Yu. Slavyanovb a Saint-Petersburg State University of Aerospace Instrumentation
b Saint-Petersburg State University
Abstract:
Euler integral transformations relate solutions of ordinary linear
differential equations and generate integral representations of the solutions
in a number of cases or relations between solutions of constrained equations
(Euler symmetries) in some other cases. These relations lead to
the corresponding symmetries of the monodromy matrices. We discuss Euler
symmetries in the case of the simplest Fuchsian system that is equivalent to
a deformed Heun equation, which is in turn related to the Painlevé PVI
equation. The existence of integral symmetries of the deformed Heun equation
leads to the corresponding symmetries of the PVI equation.
Keywords:
Euler transformation, Heun equation, Painlevé equation.
Received: 29.10.2007
Citation:
A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed Heun equation and symmetries
of the Painlevé PVI equation”, TMF, 155:2 (2008), 252–264; Theoret. and Math. Phys., 155:2 (2008), 722–733
Linking options:
https://www.mathnet.ru/eng/tmf6209https://doi.org/10.4213/tmf6209 https://www.mathnet.ru/eng/tmf/v155/i2/p252
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Abstract page: | 686 | Full-text PDF : | 216 | References: | 83 | First page: | 12 |
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