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One Dimensional Kardar-Parisi-Zhang Equation in Various Initial Condition Amplitudes

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Title: One Dimensional Kardar-Parisi-Zhang Equation in Various Initial Condition Amplitudes

Authors: Okhunjon Sayfidinov, Gabriella Bognar

Journal: Journal of advances in applied & computational mathematics

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Year: 2020

Volume: 7

Language: en

DOI: 10.15377/2409-5761.2020.07.5

Keywords: Gaussian noiseamplitudewhite noiseinitial conditionKPZ equationKPZ universality class

Categories
Stochastic Processes (111) Physics (3755) Partial Differential Equations (47) Nonlinear Dynamics (20) Statistical Mechanics (10)

Abstract

The Kardar-Parisi-Zhang (KPZ) equation with different initial conditions has been investigated in this paper. The numerical solutions using fixed data are performed without noise term and with two kinds of noise terms, i.e., Gaussian noise term and white noise term. The solutions to the equation have been simulated with different initial conditions of the form A sin (x/16) Our study introduces the obtained shape of the solutions to the KPZ equation according to noise terms with three different amplitudes A. The effect of the noise and the amplitude of the noises are presented and investigated.

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