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.
Publié le : 2004-06-14
Classification:
Isomonodromic deformation,
the first Painlevé hierarchy,
34M55,
30D35
@article{1116014786,
author = {Shimomura, Shun},
title = {A certain expression of the first Painlev\'e hierarchy},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {80},
number = {6},
year = {2004},
pages = { 105-109},
language = {en},
url = {http://dml.mathdoc.fr/item/1116014786}
}
Shimomura, Shun. A certain expression of the first Painlevé hierarchy. Proc. Japan Acad. Ser. A Math. Sci., Tome 80 (2004) no. 6, pp. 105-109. http://gdmltest.u-ga.fr/item/1116014786/