Six-dimensional Painleve systems and their particular solutions in terms of hypergeometric functions

TL;DR

This paper introduces a new class of six-dimensional Painleve systems derived from monodromy preserving deformations of Fuchsian systems, expressed as polynomial Hamiltonian systems, and explores their particular solutions using hypergeometric functions.

Contribution

It presents a novel class of six-dimensional Painleve systems and connects their solutions to hypergeometric functions, expanding the understanding of integrable systems.

Findings

New six-dimensional Painleve systems formulated as polynomial Hamiltonian systems

Explicit particular solutions expressed via hypergeometric functions

Linking monodromy preserving deformations to hypergeometric functions

Abstract

In this article, we propose a class of six-dimensional Painleve systems given as the monodromy preserving deformations of the Fuchsian systems. They are expressed as polynomial Hamiltonian systems of sixth order. We also discuss their particular solutions in terms of the hypergeometric functions defined by fourth order rigid systems.