Exact result vs. dynamic renormalization group analysis for the non-local Kardar–Parisi–Zhang equation

In this paper I discuss a generalization of the well-known Kardar–Parisi–Zhang (KPZ) equation that includes long-range interactions. This Non-local Kardar–Parisi–Zhang (NKPZ) equation has been suggested in the past to describe physical phenomena such as burning paper or deposition of colloids. I show that the steady state strong coupling solution for a subfamily of the NKPZ models can be solved exactly in one dimension, using the Fokker–Planck form of the equation, and yields a Gaussian distribution. This exact result does not agree with a previous result obtained by dynamic renormalization group (DRG) analysis. The reasons for this disagreement are not yet clear.