arXiv subjects
Publications and source records attributed to Nobuhiko Tahara.
For each Painlevé system P_J except the first one, we have a Bäcklund transformation group which is a lift of an affine Weyl group. In this paper, we show that the Bäcklund transformation groups for J=V,IV,III,II are successively obtained from that for J=VI by the well known degeneration or confluence processes.
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.