Analytic solutions of the two-dimensional Kardar-Parisi-Zhang growing equation

Imre Ferenc Barna , Gabriella Bognár , László Mátyás , Mohamed Guedda (1) , Krisztián Hriczó

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

The two-dimensional Kardar-Parisi-Zhang dynamic interface growth equation is analyzed in Cartesian coordinates with different kind of trial-functions. We show that the one-dimensional self-smilar Ansatz can be generalized for multi space dimensions is numerous ways leading to fine differences between the obtained results. The role of the noise term is discussed as well. © 2020 American Institute of Physics Inc.. All rights reserved.

Domaines: Mathématiques [math]

Imre Ferenc Barna, Gabriella Bognár, László Mátyás, Mohamed Guedda, Krisztián Hriczó. Analytic solutions of the two-dimensional Kardar-Parisi-Zhang growing equation. INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019, Sep 2019, Rhodes, Greece. pp.280002, ⟨10.1063/5.0027197⟩. ⟨hal-03691008⟩