NON-EXISTENCE OF RATIONAL SOLUTIONS OF THE SASANO SYSTEMS OF TYPES B₃⁽¹⁾ AND D₄⁽²⁾

Abstract

In this paper, we prove that the Sasano systems of types B₃⁽¹⁾ and D₄⁽²⁾ have no meromorphic solution at t =∞, which implies the non-existence of rational solutions of the systems. Sasano systems of types B₃⁽¹⁾ and D₄⁽²⁾ are the systems of ordinary differential equations whose Bäcklund transformation groups are isomorphic to the affine Weyl groups of types B₃⁽¹⁾ and D₄⁽²⁾.