kth.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV
Centre for Mathematical Sciences, Lund University, 22100 Lund, Sweden.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6191-7769
2025 (English)In: Advanced Nonlinear Studies, ISSN 1536-1365, E-ISSN 2169-0375, Vol. 25, no 1, p. 106-151Article in journal (Refereed) Published
Abstract [en]

We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term in the case when no solitons are present. In this paper, we derive an asymptotic formula in Sector IV, characterized by xt ∈ (√13, 1), in the case when solitons are present. In particular, our results provide an exact expression for the soliton-radiation interaction to leading order and a verification of the soliton resolution conjecture for the Boussinesq equation in Sector IV.

Place, publisher, year, edition, pages
Walter de Gruyter GmbH , 2025. Vol. 25, no 1, p. 106-151
Keywords [en]
Boussinesq equation, long-time asymptotics, Riemann-Hilbert problem
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-363126DOI: 10.1515/ans-2023-0154ISI: 001388155000001Scopus ID: 2-s2.0-105003027260OAI: oai:DiVA.org:kth-363126DiVA, id: diva2:1956376
Note

QC 20250507

Available from: 2025-05-06 Created: 2025-05-06 Last updated: 2025-05-07Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records

Lenells, Jonatan

Search in DiVA

By author/editor
Lenells, Jonatan
By organisation
Mathematics (Div.)
In the same journal
Advanced Nonlinear Studies
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 12 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf