Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems

Abstract

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.

11 pages, to be published in J. Math. Soc. Japan

Cited by in corpus (1)

• Coalescence, Deformation and Bäcklund Symmetries of Painlevé IV and II Equations