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

29 pages

References in corpus (4)

• Classification of Fuchsian systems and their connection problem
• Coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of type $D_6^{(1)}$, II
• A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function ${}_{n+1}{F}_n$
• Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation

Cited by in corpus (1)

• A higher order Painlevé system in two variables and extensions of the Appell hypergeometric functions $F_1$, $F_2$ and $F_3$