Relations Between Linear Equations and Painlevé’s Equations
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Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas binding these approaches are derived. Symmetries demonstrated in the equations are also a subject of discussion.
KeywordsHeun equation Heun deformed equation Apparent singularity 2×2 Fuchsian linear system Painlevé equation Antiquantization Euler integral transform
Mathematics Subject Classification32S99 33E17 33E99 34B30 81R12
The author is grateful to A.Ya. Kazakov for long cooperation and to M.V. Babich for useful discussions.