Numerical analysis of the noisy Kuramoto-Sivashinsky equation in 2+1 dimensions

The nondeterministic Kuramoto-Sivashinsky (KS) equation is solved numerically in 2+1 dimensions. The simulations reveal the presence of early and late scaling regimes. The initial-time values for the growth exponent β, the roughness exponent α, and the dynamic exponent z are found to be 0.22–0.25, 0.75–0.80, and 3.0–4.0, respectively. For long times, the scaling exponents are notably less than the exponents of the Kardar-Parisi-Zhang equation. Other properties, such as skewness and kurtosis of the height distributions, are examined. We also compare the numerical analysis with recent experimental results on ion sputtering of surfaces that can be described by the KS equation.