Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and Algebraic Solutions of the Sixth Painlevé Equation

Details Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and Algebraic Solutions of the Sixth Painlevé Equation Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and Algebraic Solutions of the Sixth Painlevé Equation

2001-07-31

arxiv.org/abs/nlin/0107074v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

26 pages

Scientific paper

10.1007/s002200200653

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 Painlev\'e equation. $RS$-Transformations of the ranks 3 and 4 of $2\times2$ matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.

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