Download or read book Painleve Equations through Symmetry written by Masatoshi Noumi and published by American Mathematical Soc.. This book was released on 2004-01-01 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the symmetry of Painleve equations (especially those of types II and IV). The author studies families of transformations for several types of Painleve equationsQthe so-called Backlund transformationsQwhich transform solutions of a given Painleve equation to solutions of the same equation with a different set of parameters. It turns out that these symmetries can be interpreted in terms of root systems associated to affine Weyl groups. The author describes the remarkable combinatorial structures of these symmetries and shows how they are related to the theory of $\tau$-functions associated to integrable systems.