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.
|Number of pages||5|
|Journal||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|Publication status||Published - 2004 Jun|
- Isomonodromic deformation
- The first Painlevé hierarchy
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