DETERMINISTIC AND STOCHASTIC SURFACE GROWTH WITH GENERALIZED NONLINEARITY

The scaling behavior of the interface width for the generalized Kardar-Parisi-Zhang (KPZ) equation partial derivative h/partial derivative t=nu del2h + lambda\del h\mu + eta(x,t) is studied in two dimensions as a function of mu with and without the additive noise term eta. In the case of additive noise, the scaling of the surface width is found for all mu to be the same as for the ordinary KPZ equation (mu=2) in contrast to a previous conjecture. This appears to be due to the combined action of the nonlinearity \del h\mu and the noise under renormalization, which together induce a \del h\2 term. For the deterministic case corresponding to the smoothing of an initially rough interface with roughness exponent alpha, good agreement with the scaling relation z=min[2,alpha(1-mu)+mu] is obtained for mu greater-than-or-equal-to 1. However, for mu < 1, an instability is observed, which leads to a fluctuating grooved surface. For an asymptotically large system, the roughness exponent is 1 and the growth exponent is approximately equal to 1/2. The evolution of two slightly different surfaces is studied in order to determine a Lyapunov exponent characterizing this instability.