  Commuting transfer matrices of $U_{q}(X_{r}^{(1)})$ vertex models obey the
functional relations which can be viewed as an $X_{r}$ type Toda field equation
on discrete space time. Based on analytic Bethe ansatz we present, for
$X_{r}=D_{r}$, a new expression of its solution in terms of determinants and
Pfaffians.
