  Ablowitz and Ladik discovered a discretization which preserves the
integrability of the nonlinear Schroedinger equation in one dimension. We
compute the generalized free energy of this model and determine the GGE
averaged fields and currents. They are linked to the mean-field circular
unitary matrix ensemble (CUE). The resulting hydrodynamic equations follow the
pattern already known from other integrable many-body systems. Studied is also
the discretized modified Korteweg-de-Vries equation which turns out to be
related to the beta Jacobi log gas.
