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

Imre F. Barna, Gabriella Bognár, Mohammed Guedda, László Mátyás, Krisztián Hriczó
2020 Mathematical Modelling and Analysis  
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
more » ... functions like Kummer, Heun, Whittaker or error functions showing a very rich mathematical structure with some common general characteristics.
doi:10.3846/mma.2020.10459 fatcat:6uea7navhzezhp33tzuh34k2ri