After a brief introduction we review the nonperturbative weak noise approach to the KPZ equation in one dimension. We argue that the strong coupling aspects of the KPZ equation are related to the existence of localized propagating domain walls or solitons representing the growth modes; the statistical weight of the excitations is governed by a dynamical action representing the generalization of...

We carry out an exact analysis of the average frequency ν+ αxi in the direction xi of positiveslope crossing of a given level α such that, h(x, t)− h̄ = α, of growing surfaces in spatial dimension d. Here, h(x, t) is the surface height at time t, and h̄ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface ...

“Suppose that we take a bin and gently and uniformly pour in granular material. As the material in the bin builds up we can identify a surface and ask the question, ‘What is the magnitude of the fluctuation in the height of surface (measured from the base of the bin)?’ Also of interest is the length scale of the surface fluctuations and how they behave dynamically as more material is added” [1]...

The equivalence transformation algebra LE for the class of equations ut − uxx = f(u, ux) is obtained. After getting the differential invariants with respect to LE , some results which allow to linearize a subclass of equations are showed. Equations like the standard deterministic KPZ equation fall in this subclass. PACS: 02.30.Jr; 02.20.Tw

We solve the large deviations of Kardar-Parisi-Zhang (KPZ) equation in one dimension at short time by introducing an approach which combines field theoretical, probabilistic and integrable techniques. expand program weak noise theory, maps onto a non-linear hydrodynamic problem, unveil its complete solvability through connection to integrability Zakharov-Shabat system. Exact solutions, dependin...