Pseudospectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation, where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique compares favorably with previous methods based on real space schemes.