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

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 were 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.

arXiv comment13 Pages and 15 Figures

References in corpus (12)

• The one-dimensional KPZ equation: an exact solution and its universality
• Free-energy distribution of the directed polymer at high temperature
• An exact solution for the KPZ equation with flat initial conditions
• Colloquium: Cluster growth on surfaces - densities, size distributions and morphologies
• Mode coupling and renormalization group results for the noisy Burgers equation
• Surface growth for molten silicon infiltration into carbon millimeter-sized channels: Lattice-Boltzmann simulations, experiments and models
• Heat conduction: a telegraph-type model with self-similar behavior of solutions II
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• A random rule model of surface growth
• Impact of anisotropic interactions on non-equilibrium cluster growth at surfaces
• Entropy production in diffusion-reaction systems: The reactive random Lorentz gas
• Suppressing correlations in massively parallel simulations of lattice models