A certain expression of the first Painlevé hierarchy

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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 languageEnglish
Pages (from-to)105-109
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Issue number6
Publication statusPublished - 2004 Jun
Externally publishedYes


  • Isomonodromic deformation
  • The first Painlevé hierarchy

ASJC Scopus subject areas

  • Mathematics(all)


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