TY - JOUR

T1 - Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV

AU - Kazakov, A. Ya

AU - Slavyanov, S. Yu

PY - 2014/5/1

Y1 - 2014/5/1

N2 - Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or relations between solutions of constrained equations. These relations lead to the corresponding symmetries of the monodromy matrices for the differential equations. We discuss Euler symmetries in the case of the deformed confluent Heun equation, which is in turn related to the Painlevé equation PV. The existence of symmetries of the linear equations leads to the corresponding symmetries of the Painlevé equation of the Okamoto type. The choice of the system of linear equations that reduces to the deformed confluent Heun equation is the starting point for the constructions. The basic technical problem is to choose the bijective relation between the system parameters and the parameters of the deformed confluent Heun equation. The solution of this problem is quite large, and we use the algebraic computing system Maple for this.

AB - Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or relations between solutions of constrained equations. These relations lead to the corresponding symmetries of the monodromy matrices for the differential equations. We discuss Euler symmetries in the case of the deformed confluent Heun equation, which is in turn related to the Painlevé equation PV. The existence of symmetries of the linear equations leads to the corresponding symmetries of the Painlevé equation of the Okamoto type. The choice of the system of linear equations that reduces to the deformed confluent Heun equation is the starting point for the constructions. The basic technical problem is to choose the bijective relation between the system parameters and the parameters of the deformed confluent Heun equation. The solution of this problem is quite large, and we use the algebraic computing system Maple for this.

KW - apparent singularity

KW - confluent Heun equation

KW - Euler integral transform

KW - monodromy

UR - http://www.scopus.com/inward/record.url?scp=84927673141&partnerID=8YFLogxK

U2 - 10.1007/s11232-014-0160-3

DO - 10.1007/s11232-014-0160-3

M3 - Article

AN - SCOPUS:84927673141

VL - 179

SP - 543

EP - 549

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -