---
OA_place: repository
OA_type: green
_id: '22026'
abstract:
- lang: eng
  text: We address two pressing questions in the theory of the Korteweg–de Vries (KdV)
    equation. First, we show the uniqueness of solutions to KdV that are merely bounded,
    without any further decay, regularity, periodicity, or almost periodicity assumptions.
    The second question, emphasized by Deift, regards whether almost periodic initial
    data leads to almost periodic solutions to KdV. Building on the new observation
    that this is false for the Airy equation, we construct an example of almost periodic
    initial data whose KdV evolution remains bounded, but fails to be almost periodic
    at a later time. Our uniqueness result ensures that the solution constructed is
    the unique development of this initial data.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andreia
  full_name: Chapouto, Andreia
  last_name: Chapouto
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: 'Chapouto A, Killip R, Vişan M. Bounded solutions of KdV: Uniqueness and the
    loss of almost periodicity. <i>Duke Mathematical Journal</i>. 2024;173(7):1227-1267.
    doi:<a href="https://doi.org/10.1215/00127094-2023-0035">10.1215/00127094-2023-0035</a>'
  apa: 'Chapouto, A., Killip, R., &#38; Vişan, M. (2024). Bounded solutions of KdV:
    Uniqueness and the loss of almost periodicity. <i>Duke Mathematical Journal</i>.
    Duke University Press. <a href="https://doi.org/10.1215/00127094-2023-0035">https://doi.org/10.1215/00127094-2023-0035</a>'
  chicago: 'Chapouto, Andreia, Rowan Killip, and Monica Vişan. “Bounded Solutions
    of KdV: Uniqueness and the Loss of Almost Periodicity.” <i>Duke Mathematical Journal</i>.
    Duke University Press, 2024. <a href="https://doi.org/10.1215/00127094-2023-0035">https://doi.org/10.1215/00127094-2023-0035</a>.'
  ieee: 'A. Chapouto, R. Killip, and M. Vişan, “Bounded solutions of KdV: Uniqueness
    and the loss of almost periodicity,” <i>Duke Mathematical Journal</i>, vol. 173,
    no. 7. Duke University Press, pp. 1227–1267, 2024.'
  ista: 'Chapouto A, Killip R, Vişan M. 2024. Bounded solutions of KdV: Uniqueness
    and the loss of almost periodicity. Duke Mathematical Journal. 173(7), 1227–1267.'
  mla: 'Chapouto, Andreia, et al. “Bounded Solutions of KdV: Uniqueness and the Loss
    of Almost Periodicity.” <i>Duke Mathematical Journal</i>, vol. 173, no. 7, Duke
    University Press, 2024, pp. 1227–67, doi:<a href="https://doi.org/10.1215/00127094-2023-0035">10.1215/00127094-2023-0035</a>.'
  short: A. Chapouto, R. Killip, M. Vişan, Duke Mathematical Journal 173 (2024) 1227–1267.
das_tickbox: '1'
date_created: 2026-06-19T07:34:05Z
date_published: 2024-05-15T00:00:00Z
date_updated: 2026-06-22T10:32:25Z
day: '15'
doi: 10.1215/00127094-2023-0035
extern: '1'
external_id:
  arxiv:
  - '2209.07501'
intvolume: '       173'
issue: '7'
keyword:
- Almost-periodic solutions
- Korteweg–de Vries
- unconditional uniqueness
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2209.07501
month: '05'
oa: 1
oa_version: Preprint
page: 1227-1267
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Bounded solutions of KdV: Uniqueness and the loss of almost periodicity'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 173
year: '2024'
...