TY - JOUR

T1 - Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation

AU - Kazakov, A. Ya

AU - Slavyanov, S. Yu

PY - 2008/5/1

Y1 - 2008/5/1

N2 - 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.

AB - 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.

KW - Euler transformation

KW - Heun equation

KW - Painlevé equation

UR - http://www.scopus.com/inward/record.url?scp=43949100661&partnerID=8YFLogxK

U2 - 10.1007/s11232-008-0062-3

DO - 10.1007/s11232-008-0062-3

M3 - Article

AN - SCOPUS:43949100661

VL - 155

SP - 722

EP - 733

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -