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 isomonodromic deformation of certain linear systems with an irregular singular point.
Citation
Shun Shimomura. "A certain expression of the first Painlevé hierarchy." Proc. Japan Acad. Ser. A Math. Sci. 80 (6) 105 - 109, June 2004. https://doi.org/10.3792/pjaa.80.105
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