From the Klein-Gordon-Zakharov system to the Klein-Gordon equation

In a singular limit the Klein-Gordon (KG) equation can be derived from the Klein-Gordon-Zakharov (KGZ) system. We point out that for the original system posed on a d-dimensional torus the solutions of the KG equation do not approximate the solutions of the KGZ system. The KG system has to be modified to make correct predictions about the dynamics of the KGZ system. We explain that this modification is not necessary for the approximation result for the whole space Rd with d _ 3.