The asymptotic behavior of solutions of the Korteweg-de Vries equation evolving from very irregular data
type: Item
instance of: scholarly article
title: The asymptotic behavior of solutions of the Korteweg-de Vries equation evolving from very irregular data
zbMATH Open document ID: 0642.35072
DOI: 10.1016/S0003-4916(87)80016-7
author: T. Kappeler
author: Amy Cohen Murray
published in: Annals of Physics
publication date: 1987-01-01T00:00:00Z
review text: The behavior of solutions of Korteweg-de Vries equation \(u_ t-6uu_ x+u_{xxx}=0\) for initial conditions \(u(x,0)=\mu (x)\) being a measure is studied. It is assumed that \(\mu\) is such that \(\int^{\infty}_{- \infty}(1+| x|)^ N d| \mu | (x)<\infty\) for \(N=3\) or \(N=4\). The main result states that if n is the number of poles of the transmission coefficient of the Schrödinger equation \(-y''+\mu (x)y=k^ 2y\), then one can specify an n-soliton solution \(u_ s(x,t)\) such that for any \(x_ 0\), \[ \sup \{| u(x,t)-u_ s(x,t)|: x\geq x_ 0\}=O(t^{-1/3}). \] The case \(n=0\) is also under discussion.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 4046284
zbMATH Keywords: inverse scattering method
zbMATH Keywords: multisoliton solutions
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: initial conditions
zbMATH Keywords: transmission coefficient
zbMATH Keywords: Schrödinger equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4046284