COMPARISON OF THE SCALE INVARIANT SOLUTIONS OF THE KURAMOTO-SIVASHINSKY AND KARDAR-PARISI-ZHANG EQUATIONS IN D-DIMENSIONS

It is shown that the scale invariant solutions of the KS and KPZ models of surface roughening are identical for dimensions d < 2, but may differ for dimensions d greater-than-or-equal-to 2 in the strong coupling limit. For d greater-than-or-equal-to 2, these models posses two different scaling solutions, one with d-independent scaling exponents y = z = 2, and the other with d-dependent nontrivial exponents The first of these solutions is realizable in one of these models, but not the other. These conclusions are valid to all orders in renormalized perturbation theory.