ANALYTIC SELF-SIMILAR SOLUTIONS OF THE KARDAR-PARISI-ZHANG INTERFACE GROWING EQUATION WITH VARIOUS NOISE TERMS-Reference-Cited by-同舟云学术

ANALYTIC SELF-SIMILAR SOLUTIONS OF THE KARDAR-PARISI-ZHANG INTERFACE GROWING EQUATION WITH VARIOUS NOISE TERMS

Published:2020-03-18 Issue:2 Volume:25 Page:241-256
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Barna Imre F.¹,Bognár Gabriella²^ORCID,Guedda Mohammed³,Mátyás László⁴^ORCID,Hriczó Krisztián²^ORCID

Affiliation:

1. Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29 - 33, H-1121 Budapest, Hungary

2. University of Miskolc, Faculty of Mechanical Engineering and Informatics, Miskolc-Egyetemváros 3515, Hungary

3. cUniversité de Picardie Jules Verne Amiens, Faculte de Mathematiques et d’Informatique, 33, rue Saint-Leu 80039 Amiens, France

4. Sapientia Hungarian University of Transylvania, Faculty of Economics, Socio-Human Sciences and Engineering, Department of Bioengineering Libertătii sq.1, 530104 Miercurea Ciuc, Romania

Abstract

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.

Publisher

Vilnius Gediminas Technical University

Subject

Modelling and Simulation,Analysis

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