This work focuses on control of surface roughness in sputtering processes including two surface micro-processes, diffusion and erosion. The fluctuation of surface height of such sputtering processes can be described by the stochastic Kuramoto–Sivashinsky equation (KSE), a fourth-order stochastic partial differential equation (PDE). Specifically, we consider sputtering processes, including surfa...

Surfaces eroded by ion sputtering are sometimes observed to develop morphologies which are either ripple (periodic) or rough (nonperiodic). We introduce a discrete stochastic model that allows us to interpret these experimental observations within a unified framework. We find that a periodic ripple morphology characterizes the initial stages of the evolution, whereas the surface displays self-a...

Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddl...

In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto–Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series solution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x, t), the initial guess, u0(x, t) and the auxiliary linear...

We have used themodified variational iterationmethod MVIM to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrodinger-KdV equations, and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the mod...