Rational solutions of the Sasano systems of types $B_4^{(1)},$ $D_4^{(1)}$ and $D_5^{(2)}$

Abstract

We classify the rational solutions of the Sasano systems of types $B_4^{(1)},$ $D_4^{(1)}$ and $D_5^{(2)},$ which are all given by the coupled $P_{\mathrm{III}}$ systems and have the affine Weyl group symmetries of types $B_4^{(1)},$ $D_4^{(1)}$ and $D_5^{(2)}.$ The rational solutions are classified as one type by the Bäcklund transformation groups.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1103.4906, arXiv:1103.4906. See the Remark of page 5 in Introduction