Kinetic roughening model with opposite Kardar-Parisi-Zhang   nonlinearities
  We introduce a model that simulates a kinetic roughening process with two kinds of particles: one follows the ballistic deposition (BD) kinetic and, the other, the restricted solid-on-solid (KK) kinetic. Both of these kinetics are in the universality class of the nonlinear KPZ equation, but the BD kinetic has a positive nonlinear constant while the KK kinetic has a negative one. In our model, called BD-KK model, we assign the probabilities p and (1-p) to the KK and BD kinetics, respectively. For a specific value of p, the system behaves as a quasi linear model and the up-down symmetry is recuperated. We show that nonlinearities of odd-order are relevant in these low nonlinear limit. 
T. J. da Silva and J. G. Moreira