Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit

Abstract

A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized growth modes with superimposed diffusive modes. Applying Derrick's theorem it is conjectured that the upper critical dimension is four.

10 pages in revtex and 2 figures in eps, a few typos corrected

References in corpus (1)

• Correlations, soliton modes, and non-Hermitian linear mode transmutation in the 1D noisy Burgers equation

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