Solitons and shock waves under random external noise
type: Item
instance of: scholarly article
title: Solitons and shock waves under random external noise
zbMATH Open document ID: 0727.60067
DOI: 10.1016/0034-4877(89)90036-0
author: K. Sobczyk
author: A. Orłowski
published in: Reports on Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The paper treats nonlinear wave processes under random external noise. The two basic equations considered are the Korteweg-de Vries and Burgers equations, governing nonlinear wave processes with dispersion and dissipation, respectively. A basic feature of these equations is the existence of stable wave profiles, called solitons, and shock waves, respectively in the two cases. Under additive noise perturbation (depending only on time) it is shown that a suitable change of variable reduces the stochastic equation to a deterministic one of classical form. The stationary random solution (soliton or shock wave) obtained explicitly by this procedure is a function of the noise. Mean and variance of this random wave are in exact or approximated form, and graphically illustrated. Among the results of physical significance, it is shown that the noise causes damping of the solitons.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76M35
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 4201297
zbMATH Keywords: nonlinear wave processes
zbMATH Keywords: existence of stable wave profiles
zbMATH Keywords: shock wave
reviewed by: Franco Flandoli
MaRDI profile type: Publication
full work available at URL: 0034-4877(89)90036-0
OpenAlex ID: W2006985219
cites work: Q3947997
cites work: Q3692560
cites work: A generalization of the construction of the class operator
cites work: Q4123597
description: scientific article; zbMATH DE number 4201297