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Zbl 1019.34086
Andreev, F.V.; Kitaev, A.V.
Transformations $RS_4^2(3)$ of the ranks $\le 4$ and algebraic solutions of the sixth Painlevé equation. (English)
[J] Commun. Math. Phys. 228, No.1, 151-176 (2002). ISSN 0010-3616; ISSN 1432-0916/e

Considerable attention has been paid to the search of algebraic solutions to the sixth Painlevé equation. Here, compositions of rational transformations of independent variables of linear matrix ODEs with the Schlesinger transformations (RS-transformations) are used to construct algebraic solutions to Painlevé VI. RS-transformations of ranks $3$ and $4$ of $2\times 2$-matrix Fuchsian ODEs with $3$ singular points into analogous ODEs with $4$ singular points are classified.
[Mircea Crâşmăreanu (Iasi)]

MSC 2000:: *34M55 Painlevé and other special equations
33E17 Painlevé-type functions
34M25 Formal solutions, transform techniques

Keywords: Painlevé VI; RS-transformation; Fuchsian ordinary differential equation

Cited in: Zbl 1111.34065

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