Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation

TL;DR

This paper presents a higher order Painleve system of type D^{(1)}_{2n+2} as a monodromy preserving deformation of a Fuchsian system, extending the sixth Painleve equation with affine Weyl group symmetry.

Contribution

It formulates the higher order Painleve system of type D^{(1)}_{2n+2} explicitly as a monodromy preserving deformation, connecting algebraic geometry and integrable systems.

Findings

Established the monodromy preserving deformation framework for the system.

Extended the sixth Painleve equation to higher order systems.

Linked algebraic geometry with Painleve systems through Fuchsian systems.

Abstract

The higher order Painleve system of type D^{(1)}_{2n+2} was proposed by Y. Sasano as an extension of the sixth Painleve equation for the affine Weyl group symmetry with the aid of algebraic geometry for Okamoto initial value space. In this article, we give it as the monodromy preserving deformation of a Fuchsian system.