### Abstract

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 isomonodrornic deformation of certain linear systems with an irregular singular point.

Original language | English |
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Pages (from-to) | 105-109 |

Number of pages | 5 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 80 |

Issue number | 6 |

Publication status | Published - 2004 Jun |

### Fingerprint

### Keywords

- Isomonodromic deformation
- The first Painlevé hierarchy

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Japan Academy Series A: Mathematical Sciences*,

*80*(6), 105-109.

**A certain expression of the first Painlevé hierarchy.** / Shimomura, Shun.

Research output: Contribution to journal › Article

*Proceedings of the Japan Academy Series A: Mathematical Sciences*, vol. 80, no. 6, pp. 105-109.

}

TY - JOUR

T1 - A certain expression of the first Painlevé hierarchy

AU - Shimomura, Shun

PY - 2004/6

Y1 - 2004/6

N2 - 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 isomonodrornic deformation of certain linear systems with an irregular singular point.

AB - 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 isomonodrornic deformation of certain linear systems with an irregular singular point.

KW - Isomonodromic deformation

KW - The first Painlevé hierarchy

UR - http://www.scopus.com/inward/record.url?scp=6344255044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=6344255044&partnerID=8YFLogxK

M3 - Article

VL - 80

SP - 105

EP - 109

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 6

ER -