SIMILARITY REDUCTIONS OF INTEGRABLE LATTICES AND DISCRETE ANALOGS OF THE PAINLEVE-II EQUATION

Using the direct linearization method similarity reductions of integrable lattices are constructed providing discrete analogues of the Painleve II equation. The reduction is obtained by imposing an non-autonomous integrable constraint on the corresponding lattice equations, which are differential-difference analogue of the KdV and modified KdV equation. An isomonodromic deformation problem for these systems is derived. It is shown how this system in an appropriate continuum limit reduces to the PII equation.