  We discuss an interrelation between quantum integrable models and classical
soliton equations with discretized time. It appeared that spectral
characteristics of quantum integrable systems may be obtained from entirely
classical set up. Namely, the eigenvalues of the quantum transfer matrix and
the scattering $S$-matrix itself are identified with a certain $\tau$-functions
of the discrete Liouville equation. The Bethe ansatz equations are obtained as
dynamics of zeros. For comparison we also present the Bethe ansatz equations
for elliptic solutions of the classical discrete Sine-Gordon equation. The
paper is based on the recent study of classical integrable structures in
quantum integrable systems, hep-th/9604080.
