Bäcklund Transformations of the Sixth Painlevé Equation in Terms of Riemann-Hilbert Correspondence
نویسندگان
چکیده
It is well known that the sixth Painlevé equation PVI admits a group of Bäcklund transformations which is isomorphic to the affine Weyl group of type D (1) 4 . Although various aspects of this unexpectedly large symmetry have been discussed by many authors, there still remains a basic problem yet to be considered, that is, the problem of characterizing the Bäcklund transformations in terms of Riemann-Hilbert correspondence. In this direction, we show that the Bäcklund transformations are just the pull-back of very simple transformations on the moduli of monodromy representations by the RiemannHilbert correspondence. This result gives a natural and clear picture of the Bäcklund transformations.
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