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Nonlinear chains and Painlevé equations. (English) Zbl 0812.34030
Summary: ODE systems which define a periodically closed sequence of Bäcklund transformations (BT) and which are equivalent to the Painlevé equations \(P_ 2- P_ 6\) are presented. Transformation properties of Painlevé equations can be easily derived from the discrete symmetries of these systems.

MSC:
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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