  We expand a partial difference equation (P$\Delta$E) on multiple lattices and
obtain the P$\Delta$E which governs its far field behaviour. The
perturbative--reductive approach is here performed on well known nonlinear
P$\Delta$Es, both integrable and non integrable. We study the cases of the
lattice modified Korteweg--de Vries (mKdV) equation, the Hietarinta equation,
the lattice Volterra--Kac--Van Moerbeke (VKVM) equation and a non integrable
lattice KdV equation. Such reductions allow us to obtain many new P$\Delta$Es
of the nonlinear Schr\"odinger (NLS) type.
