Proceedings of the Japan Academy, Series A, Mathematical Sciences

Auxiliary differential polynomials for the first Painlevé hierarchy

Yoshikatsu Sasaki

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This article concerns with the first Painlevé hierarchy, i.e. the $2n$-th order analogues of the first Painlevé equation. Several higher order analogues of the first Painlevé equation are proposed by several authors however, we investigate one derived from the KdV hierarchy by studying singularity manifold. We give the auxiliary differential polynomials of the first Painlevé hierarchy.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 1 (2015), 7-8.

First available in Project Euclid: 5 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34M55: Painlevé and other special equations; classification, hierarchies;
Secondary: 33E17: Painlevé-type functions

Painlevé hierarchy differential polynomials


Sasaki, Yoshikatsu. Auxiliary differential polynomials for the first Painlevé hierarchy. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 1, 7--8. doi:10.3792/pjaa.91.7.

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