The korteweg-de vries equation at H-1regularity

Tristan J. Buckmaster, Herbert Koch

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H-1 initial data; moreover, we will study the problem of orbital and asymptotic Hs stability of solitons for integers s≥-1; finally, we will also prove new a priori H-1 bound for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation.

Original languageEnglish (US)
Pages (from-to)1071-1098
Number of pages28
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume32
Issue number5
DOIs
StatePublished - Sep 1 2015

Fingerprint

Korteweg-de Vries equation
Korteweg-de Vries Equation
Existence of Weak Solutions
Initial value problems
Modified Equations
Asymptotic stability
Solitons
Real Line
Asymptotic Stability
Initial Value Problem
Integer

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Mathematical Physics

Keywords

  • Korteweg-de Vries equation
  • Miura map
  • Stability of solitons

Cite this

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The korteweg-de vries equation at H-1regularity. / Buckmaster, Tristan J.; Koch, Herbert.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 32, No. 5, 01.09.2015, p. 1071-1098.

Research output: Contribution to journalArticle

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