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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 155, Number 2, Pages 252–264
DOI: https://doi.org/10.4213/tmf6209 (Mi tmf6209) 		 
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
Full-text PDF (462 kB) Citations (23)
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DOI: https://doi.org/10.4213/tmf6209
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
English version:
Theoretical and Mathematical Physics, 2008, Volume 155, Issue 2, Pages 722–733
DOI: https://doi.org/10.1007/s11232-008-0062-3
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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