Nonlinear chains and Painlevé equations. (English) Zbl 0812.34030

Adler, V. E.

Physica D 73, No. 4, 335-351 (1994).

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.

Keywords:

transformation properties; periodically closed sequence of Bäcklund transformations; Painlevé equations; discrete symmetries

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