An augmentation of the phase space of the system of type A^{(1)}_4

Abstract

We investigate the differential system with affine Weyl group symmetry of type A^{(1)}_4 and construct a space which parametrizes all meromorphic solutions of it. To demonstrate our method based on singularity analysis and affine Weyl group symmetry, we first study the system of type A^{(1)}_2, which is the equivalent of the fourth Painlevé equation, and obtain the space which augments the original phase space of the system by adding spaces of codimension 1. For the system of type A^{(1)}_4, codimension 2 spaces should be added to the phase space of the system in addition to codimension 1 spaces.

21 pages, to be published in Kyushu J. Math

References in corpus (1)

• Higher order Painlevé equations of type $A_l^{(1)}$

Cited by in corpus (16)

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• Studies on the Garnier system in two variables
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• Coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of types $B_6^{(1)}$, $D_6^{(1)}$ and $D_7^{(2)}$
• Coupled Painlevé II Systems in Dimension 4 and the systems of type ${A_4}^{(1)}$
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• On some Hamiltonian structures of coupled Painlevé II systems in dimension four
• Remark on the Garnier system in two variables
• Five-parameter family of partial differential systems in two variables