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Generalized discretization of the Kardar-Parisi-Zhang equation

R. C. Buceta
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Abstract

We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any discretization scheme. We show that the discretization prescription is a consequence of each particular model. From the ballistic deposition model we derive the discretization prescription of the corresponding KPZ equation.

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R. C. Buceta. 2004-10-20. Generalized discretization of the Kardar-Parisi-Zhang equation. https://doi.org/10.1103/physreve.72.017701

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