Higher order Painleve system of type D^{(1)}_{2n+2} arising from integrable hierarchy

TL;DR

This paper derives a higher order Painleve system of type D^{(1)}_{2n+2} from a Drinfeld-Sokolov hierarchy, extending Painleve VI and exploring its Hamiltonian structure with affine Weyl symmetry.

Contribution

It provides a derivation of the higher order Painleve system from integrable hierarchies, connecting it to affine Weyl group symmetries and Hamiltonian formulations.

Findings

Derivation of the system from Drinfeld-Sokolov hierarchy

Connection to affine Weyl group symmetry

Hamiltonian formulation of the higher order Painleve system

Abstract

A higher order Painleve system of type D^{(1)}_{2n+2} was introduced by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry. It is also expressed as a Hamiltonian system of order 2n with a coupled Painleve VI Hamiltonian. In this paper, we discuss a derivation of this system from a Drinfeld-Sokolov hierarchy.