Communications in Mathematical Physics

, Volume 228, Issue 1, pp 151–176 | Cite as

Transformations RS42(3) of the Ranks ≤ 4¶and Algebraic Solutions of the Sixth Painlevé Equation

  • F. V. Andreev
  • A. V. Kitaev


Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations (RS-transformations) are used to construct algebraic solutions of the sixth Painlevé equation. RS-Transformations of the ranks 3 and 4 of 2 × 2 matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.


Differential Equation Ordinary Differential Equation Singular Point Linear Matrix Rational Transformation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • F. V. Andreev
    • 1
  • A. V. Kitaev
    • 2
  1. 1.Steklov Mathematical Institute, Fontanka 27, 191011 St.Petersburg, Russia. E-mail: kitaev@pdmi.ras.ruRU
  2. 2.Western Illinois University, Department of Mathematics, Macomb, IL 61455, USA.¶E-mail: F-Andreev@wiu.eduUS

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