Higher Order Painlevé System of Type $D_{2n+2}^{(1)}$ Arising from Integrable Hierarchy

A higher order Painlevé system of type $D_{2n+2}^{(1)}$ 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.