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

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 $P_{\rm III}$ 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 B\"acklund transformation groups.