Multiple-scale analysis of discrete nonlinear partial difference   equations: the reduction of the lattice potential KdV
  We consider multiple lattices and functions defined on them. We introduce slow varying conditions for functions defined on the lattice and express the variation of a function in terms of an asymptotic expansion with respect to the slow varying lattices.   We use these results to perform the multiple--scale reduction of the lattice potential Korteweg--de Vries equation. 
D. Levi