Solutions of the Korteweg-de Vries equation with steplike initial data
type: Item
instance of: scholarly article
title: Solutions of the Korteweg-de Vries equation with steplike initial data
zbMATH Open document ID: 0598.35118
DOI: 10.1016/0022-0396(86)90059-8
author: T. Kappeler
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The Cauchy problem for the Korteweg-de Vries equation is considered where the initial profile u is a steplike function (i.e. there exist a,b in \({\mathbb{R}}\) such that \[ \int^{0}_{-\infty}| u(x)-a| (1+| x|)^ N dx<\infty \quad and\quad \int^{\infty}_{0}| u(x)- b| (1+| x|)^ N dx<\infty). \] Classical solutions are constructed for \(N\geq 3\).
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 3964569
zbMATH Keywords: inverse scattering method
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: Classical solutions
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90059-8
OpenAlex ID: W2004777940
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description: scientific article; zbMATH DE number 3964569