RATIONAL SOLUTIONS OF THE SASANO SYSTEMS OF TYPES B₄⁽¹⁾, D₄⁽¹⁾AND D₅⁽²⁾

Abstract

In this paper, we completely classify the rational solutions of the Sasano system of types B₄⁽¹⁾, D₄⁽¹⁾ and D₅⁽²⁾, which are all given by coupled P_III systems and have the affine Weyl group symmetries of types B₄⁽¹⁾, D₄⁽¹⁾ and D₅⁽²⁾. The rational solutions are classified as one type by the Bäcklund transformation group.