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Commuting transfer matrices of $U_{q}(X_{r}^{(1)})$ vertex models obey thefunctional relations which can be viewed as an $X_{r}$ type Toda field equationon 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 andPfaffians.Comment: Latex, 14 pages, ioplppt.sty and iopl12.sty assume

Solutions of a discretized Toda field equation for from analytic Bethe ansatz