Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The soliton resolution conjecture for the Boussinesq equation

Charlier, C. LU and Lenells, J. LU (2024) In Journal des Mathematiques Pures et Appliquees 191.
Abstract

We analyze the Boussinesq equation on the line with Schwartz initial data belonging to the physically relevant class of global solutions. In a recent paper, we determined ten main asymptotic sectors describing the large (x,t)-behavior of the solution, and for each of these sectors we provided the leading order asymptotics in the case when no solitons are present. In this paper, we give a formula valid in the asymptotic sector x/t∈(1,M], where M is a large positive constant, in the case when solitons are present. Combined with earlier results, this validates the soliton resolution conjecture for the Boussinesq equation everywhere in the (x,t)-plane except in a number of small transition zones.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Asymptotics, Boussinesq equation, Initial value problem, Riemann–Hilbert problem
in
Journal des Mathematiques Pures et Appliquees
volume
191
article number
103621
publisher
Elsevier Masson SAS
external identifiers
  • scopus:85208249655
ISSN
0021-7824
DOI
10.1016/j.matpur.2024.103621
language
English
LU publication?
yes
id
9ae35eef-6a36-45e8-832e-332544484fe7
date added to LUP
2024-12-10 13:53:47
date last changed
2025-04-04 14:06:57
@article{9ae35eef-6a36-45e8-832e-332544484fe7,
  abstract     = {{<p>We analyze the Boussinesq equation on the line with Schwartz initial data belonging to the physically relevant class of global solutions. In a recent paper, we determined ten main asymptotic sectors describing the large (x,t)-behavior of the solution, and for each of these sectors we provided the leading order asymptotics in the case when no solitons are present. In this paper, we give a formula valid in the asymptotic sector x/t∈(1,M], where M is a large positive constant, in the case when solitons are present. Combined with earlier results, this validates the soliton resolution conjecture for the Boussinesq equation everywhere in the (x,t)-plane except in a number of small transition zones.</p>}},
  author       = {{Charlier, C. and Lenells, J.}},
  issn         = {{0021-7824}},
  keywords     = {{Asymptotics; Boussinesq equation; Initial value problem; Riemann–Hilbert problem}},
  language     = {{eng}},
  publisher    = {{Elsevier Masson SAS}},
  series       = {{Journal des Mathematiques Pures et Appliquees}},
  title        = {{The soliton resolution conjecture for the Boussinesq equation}},
  url          = {{http://dx.doi.org/10.1016/j.matpur.2024.103621}},
  doi          = {{10.1016/j.matpur.2024.103621}},
  volume       = {{191}},
  year         = {{2024}},
}