Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise terms

    Imre F. Barna Affiliation
    ; Gabriella Bognár   Affiliation
    ; Mohammed Guedda Affiliation
    ; László Mátyás   Affiliation
    ; Krisztián Hriczó   Affiliation


The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as various noise distribution functions. Six different cases were investigated among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions are evaluated and analyzed for all cases. All results are expressible with various special functions like Kummer, Heun, Whittaker or error functions showing a very rich mathematical structure with some common general characteristics.

Keyword : self-similar solution, KPZ equation, Gaussian noise, Lorentzian noise, special functions, Heun functions

How to Cite
Barna, I. F., Bognár, G., Guedda, M., Mátyás, L., & Hriczó, K. (2020). Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise terms. Mathematical Modelling and Analysis, 25(2), 241-256.
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Mar 18, 2020
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