---
OA_place: repository
OA_type: green
_id: '22069'
abstract:
- lang: eng
  text: "For slowly-varying initial data, solutions to the Ablowitz–Ladik system have
    been proven to converge to solutions of the cubic Schrödinger equation. In this
    paper we show that in the continuum limit, solutions to the Ablowitz–Ladik system
    with H^1 initial data may also converge to solutions of the modified Korteweg–de
    Vries equation. To exhibit this new limiting behavior, it suffices that the initial
    data is supported near the inflection points of the dispersion relation associated
    with the Ablowitz–Ladik system.\r\n\r\nOur arguments employ harmonic analysis
    tools, Strichartz estimates, and the conservation of mass and energy. Correspondingly,
    they are applicable beyond the completely integrable models of greatest interest
    to us."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Zhimeng
  full_name: Ouyang, Zhimeng
  last_name: Ouyang
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
- first_name: Lei
  full_name: Wu, Lei
  last_name: Wu
citation:
  ama: Killip R, Ouyang Z, Vişan M, Wu L. The modified Korteweg–de Vries limit of
    the Ablowitz–Ladik system. <i>Discrete and Continuous Dynamical Systems</i>. 2025;45(3):821-846.
    doi:<a href="https://doi.org/10.3934/dcds.2024114">10.3934/dcds.2024114</a>
  apa: Killip, R., Ouyang, Z., Vişan, M., &#38; Wu, L. (2025). The modified Korteweg–de
    Vries limit of the Ablowitz–Ladik system. <i>Discrete and Continuous Dynamical
    Systems</i>. American Institute of Mathematical Sciences. <a href="https://doi.org/10.3934/dcds.2024114">https://doi.org/10.3934/dcds.2024114</a>
  chicago: Killip, Rowan, Zhimeng Ouyang, Monica Vişan, and Lei Wu. “The Modified
    Korteweg–de Vries Limit of the Ablowitz–Ladik System.” <i>Discrete and Continuous
    Dynamical Systems</i>. American Institute of Mathematical Sciences, 2025. <a href="https://doi.org/10.3934/dcds.2024114">https://doi.org/10.3934/dcds.2024114</a>.
  ieee: R. Killip, Z. Ouyang, M. Vişan, and L. Wu, “The modified Korteweg–de Vries
    limit of the Ablowitz–Ladik system,” <i>Discrete and Continuous Dynamical Systems</i>,
    vol. 45, no. 3. American Institute of Mathematical Sciences, pp. 821–846, 2025.
  ista: Killip R, Ouyang Z, Vişan M, Wu L. 2025. The modified Korteweg–de Vries limit
    of the Ablowitz–Ladik system. Discrete and Continuous Dynamical Systems. 45(3),
    821–846.
  mla: Killip, Rowan, et al. “The Modified Korteweg–de Vries Limit of the Ablowitz–Ladik
    System.” <i>Discrete and Continuous Dynamical Systems</i>, vol. 45, no. 3, American
    Institute of Mathematical Sciences, 2025, pp. 821–46, doi:<a href="https://doi.org/10.3934/dcds.2024114">10.3934/dcds.2024114</a>.
  short: R. Killip, Z. Ouyang, M. Vişan, L. Wu, Discrete and Continuous Dynamical
    Systems 45 (2025) 821–846.
das_tickbox: '1'
date_created: 2026-06-19T08:20:28Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2026-06-30T07:34:20Z
day: '01'
ddc:
- '500'
doi: 10.3934/dcds.2024114
extern: '1'
external_id:
  arxiv:
  - '2404.02366'
intvolume: '        45'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2404.02366
mathsc:
- 37J70
- 37K10
- 37K60
- 35Q53
- 35Q55
month: '03'
oa: 1
oa_version: Preprint
page: 821-846
publication: Discrete and Continuous Dynamical Systems
publication_identifier:
  eissn:
  - 1553-5231
  issn:
  - 1078-0947
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: The modified Korteweg–de Vries limit of the Ablowitz–Ladik system
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2025'
...