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...

The controversy whether or not the Kardar–Parisi–Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above...

In this paper, I analyze a generalization of the molecular-beam-epitaxy equation (with spatially correlated noise) that takes into account long-range interactions of a volume conserving surface. This equation is, therefore, called the non-local molecular-beam-epitaxy (NMBE) equation, sometimes...

In this paper we discuss nonlocal growth equations such as the generalization of the Kardar–Parisi–Zhang (KPZ) equation that includes long-range interactions, also known as the Nonlocal-Kardar–Parisi–Zhang (NKPZ) equation, and the nonlocal version of the molecular-beam-epitaxy (NMBE)...