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Analytic Traveling-Wave Solutions of the Kardar-Parisi-Zhang Interface Growing Equation with Different Kind of Noise Terms

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

Abstract

The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the traveling-wave 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 Mathieu, Bessel, Airy or Whittaker functions showing a very rich mathematical structure with some common general characteristics. This study is the continuation of our former work, where the same physical phenomena was investigated with the self-similar Ansatz. The differences and similarities among the various solutions are enlightened.

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Acknowledgements

This work was supported by project no. 129257 implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the \(K \_ 18\) funding scheme. The described study was carried out as part of the EFOP-3.6.1-16-00011 “Younger and Renewing University—Innovative Knowledge City—institutional development of the University of Miskolc aiming at intelligent specialization” project implemented in the framework of the Szechenyi 2020 program. The realization of this project is supported by the European Union, co-financed by the European Social Fund.

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Authors and Affiliations

  1. Wigner Research Center, P.O. Box 49, Budapest, 1525, Hungary

    I. F. Barna

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

    G. Bognár

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

    L. Mátyás

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

    M. Guedda

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

    K. Hriczó

Authors
  1. I. F. Barna
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  2. G. Bognár
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  3. L. Mátyás
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  4. M. Guedda
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  5. K. Hriczó
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Corresponding author

Correspondence to G. Bognár .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Barna, I.F., Bognár, G., Mátyás, L., Guedda, M., Hriczó, K. (2020). Analytic Traveling-Wave Solutions of the Kardar-Parisi-Zhang Interface Growing Equation with Different Kind of Noise Terms. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_19

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