Dynamical properties of a nonlinear growth equation

TL;DR

This paper investigates the nonlinear conserved Kuramoto-Sivashinsky equation as a model for amorphous thin film growth, analyzing solution properties and surface pattern evolution through analytical and numerical methods in one- and two-dimensions.

Contribution

It provides new analytical insights into wavelength and amplitude characteristics and demonstrates surface roughening and coarsening via numerical simulations.

Findings

Analytical results on wavelength and amplitude

Surface roughening and coarsening observed

Evolution of surface morphology over time

Abstract

The conserved Kuramoto-Sivashinsky equation is considered as the evolution equation of amorphous thin film growth in one- and in two-dimensions. The role of the nonlinear term $\Delta (\ | \nabla u\ | ^{2})$ and the properties of the solutions are investigated analytically and numerically. We provide analytical results on the wavelength and amplitude. We present numerical simulations to this equation which show the roughening and coarsening of the surface pattern and the evolution of the surface morphology in time for different parameter values in one- and in two-dimensions.