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.


Hans C. Fogedby
"Localized growth modes, dynamic textures,
and upper critical dimension for the
Kardar-Parisi-Zhang equation in the weak noise limit"
Phys. Rev. Lett. 94, 195702 (2005)

"Kardar-Parisi-Zhang equation in the
weak noise limit: Pattern formation and upper critical dimension"
Phys. Rev. E 73, 031104 (2006)