Abstract
We investigate the differential system with affine Weyl group symmetry of type A_4^{(1)} 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_2^{(1)}, 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_4^{(1)}, codimension 2 spaces should be added to the phase space of the system in addition to codimension 1 spaces.
Related Links
- http://www.jstage.jst.go.jp/article/kyushujm/58/2/58_393/_article - Kyushu Journal of Mathematics, Vol. 58, pp.393-425 (2004).