Self-similar solutions for the Kardar-Parisi-Zhang interface dynamic   equation
  In this article we will present a study of the well-known Kardar-Parisi-Zhang(KPZ) model. Under certain conditions we have found analytic self-similar solutions for the underlying equation. The results are strongly related to the error functions. One and two spatial dimensions are considered with different kind of self-similar Ansaetze. 
Imre Ferenc Barna and Laszlo Matyas
nlin.AO