The korteweg-de vries equation at H-1regularity

Tristan Buckmaster, Herbert Koch

Research output: Contribution to journalArticle

7 Scopus citations

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
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

Keywords

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

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