Patterns in the Kardar–Parisi–Zhang equation
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.
Volume 96, 2022
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