Self-similar solutions for the Kardar-Parisi-Zhang interface dynamic equation
Imre Ferenc Barna, Laszlo Matyas
TL;DR
This paper investigates the KPZ interface equation, deriving analytic self-similar solutions in one and two dimensions, highlighting their relation to error functions and expanding understanding of interface dynamics.
Contribution
It presents new analytic self-similar solutions for the KPZ equation in different dimensions, using novel ansatzes and linking solutions to error functions.
Findings
Analytic self-similar solutions derived for KPZ in 1D and 2D
Solutions are expressed in terms of error functions
Different ansatzes yield distinct solution forms
Abstract
In this article we will present a study of the well-known Kardar-Parisi-Zhang(KPZ) model. Under certain conditions we have found analytic self-similar solutions for the underlying equation. The results are strongly related to the error functions. One and two spatial dimensions are considered with different kind of self-similar Ansaetze.
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Taxonomy
TopicsNonlinear Waves and Solitons · Differential Equations and Numerical Methods · Fractional Differential Equations Solutions