Comparison of the scale invariant solutions of the Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations inddimensions

Abstract

It is shown that the scale invariant solutions of the KS and KPZ models of surface roughening are identical for dimensions d2 in the strong coupling limit. For d>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.