Dynamical properties of a nonlinear Kuramoto–Sivashinsky growth equation

The conserved Kuramoto–Sivashinsky equation can be considered as the one- and two-dimensional evolution equation for amorphous thin film growth. The role of the nonlinear term Δ(∇u2) and the properties of the solutions are investigated analytically and numerically. Analytical results of wavelength and amplitude are provided. Numerical simulations of this equation are presented, showing the roughening and coarsening of the surface pattern and the evolution of the surface morphology over time for different parameter values in one- and two-dimensions.