  We study the weak interaction between a pair of well-separated coherent
structures in possibly non-local lattice differential equations. In particular
we prove that if a lattice differential equation in one space dimension has
asymptotically stable (in the sense of Chow, Mallet-Paret and Shen) traveling
wave solutions whose profiles approach limiting equilibria exponentially fast,
then the system admits solutions which are nearly the linear superposition of
two such traveling waves moving in opposite directions away from one another.
Moreover, such solutions are themselves asymptotically stable. This result is
meant to complement analytic or numeric studies into interactions of such
pulses over finite times which might result in the scenario treated here. Since
the traveling waves are moving in opposite directions, these solutions are not
shift-periodic and hence the framework of Chow, Mallet-Paret, and Shen does not
apply. We overcome this difficulty by embedding the original system in a larger
one wherein the linear part can be written as a shift-periodic piece plus
another piece which, even though it is non-autonomous and large, has certain
properties which allow us to treat it as if it were a small perturbation.
