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.

Original languageEnglish
Pages (from-to)543-549
Number of pages7
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume179
Issue number2
DOIs
StatePublished - 1 May 2014

    Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

    Research areas

  • apparent singularity, confluent Heun equation, Euler integral transform, monodromy

ID: 41346983