The korteweg-de vries equation at H-1regularity

Tristan Buckmaster; Herbert Koch

doi:10.1016/j.anihpc.2014.05.004

The korteweg-de vries equation at H^-1regularity

Tristan Buckmaster, Herbert Koch

Mathematics

Research output: Contribution to journal › Article › peer-review

13 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 H^s 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 language	English (US)
Pages (from-to)	1071-1098
Number of pages	28
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	32
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2014.05.004
State	Published - Sep 1 2015

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

Keywords

Korteweg-de Vries equation
Miura map
Stability of solitons

Access to Document

10.1016/j.anihpc.2014.05.004

Cite this

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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.",

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AU - Koch, Herbert

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AB - 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.

KW - Korteweg-de Vries equation

KW - Miura map

KW - Stability of solitons

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