Proceedings of the Japan Academy, Series A, Mathematical Sciences

A certain expression of the first Painlevé hierarchy

Shun Shimomura

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We show that each equation in the first Painlevé hierarchy is equivalent to a system of nonlinear equations determined by a kind of generating function, and that it admits the Painlevé property. Our results are derived from the fact that the first Painlevé hierarchy follows from isomonodromic deformation of certain linear systems with an irregular singular point.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 6 (2004), 105-109.

First available in Project Euclid: 13 May 2005

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Zentralblatt MATH identifier

Primary: 34M55: Painlevé and other special equations; classification, hierarchies;
Secondary: 30D35: Distribution of values, Nevanlinna theory

Isomonodromic deformation the first Painlevé hierarchy


Shimomura, Shun. A certain expression of the first Painlevé hierarchy. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 6, 105--109. doi:10.3792/pjaa.80.105.

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