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 Painlev\'e 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.