## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Auxiliary differential polynomials for the first Painlevé hierarchy

Yoshikatsu Sasaki

#### Abstract

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

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

Dates
First available in Project Euclid: 5 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1420466271

Digital Object Identifier
doi:10.3792/pjaa.91.7

Mathematical Reviews number (MathSciNet)
MR3296592

Zentralblatt MATH identifier
1316.34098

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

#### Citation

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. https://projecteuclid.org/euclid.pja/1420466271

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