We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many-body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence of an upper critical dimension.
KeywordsScaling weak noise growth modes dynamical network upper critical dimension nonlinear Schrödinger equation domain walls solitons dispersion diffusive modes
PACS Nos05.40.-a 02.50.-r 05.45.Yv 05.90.+m
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