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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

Abstract:

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.

Keywords

Differential Equation Ordinary Differential Equation Singular Point Linear Matrix Rational Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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