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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm129, 21 pages, doi:10.1093/imrn/rnm129 published on January 28, 2008
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Copyright © The Author 2008. Published by Oxford University Press.

Higher Order Painlevé System of Type Formula Arising from Integrable Hierarchy

Kenta Fuji

Takao Suzuki

Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Correspondence: Correspondence to be sent to: suzukit{at}math.kobe-u.ac.jp

A higher order Painlevé system of type Formula was introduced by Y. Sasano. It is an extension of the sixth Painlevé equation (PVI) for the affine Weyl group symmetry. It is also expressed as a Hamiltonian system of order 2n with a coupled Hamiltonian of PVI. In this article, we discuss a derivation of this system from a Drinfeld–Sokolov hierarchy.

communicated by Prof. Michio Jimbo


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