---
OA_place: repository
OA_type: green
_id: '22046'
abstract:
- lang: eng
  text: We show that solutions to the Ablowitz–Ladik system converge to solutions
    of the cubic nonlinear Schrödinger equation for merely L2 initial data. Furthermore,
    we consider initial data for this lattice model that excites Fourier modes near
    both critical points of the discrete dispersion relation and demonstrate convergence
    to a decoupled system of nonlinear Schrödinger equations.
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. Continuum limit for the Ablowitz–Ladik system.
    <i>Nonlinearity</i>. 2023;36(7):3751-3775. doi:<a href="https://doi.org/10.1088/1361-6544/acd978">10.1088/1361-6544/acd978</a>
  apa: Killip, R., Ouyang, Z., Vişan, M., &#38; Wu, L. (2023). Continuum limit for
    the Ablowitz–Ladik system. <i>Nonlinearity</i>. IOP Publishing. <a href="https://doi.org/10.1088/1361-6544/acd978">https://doi.org/10.1088/1361-6544/acd978</a>
  chicago: Killip, Rowan, Zhimeng Ouyang, Monica Vişan, and Lei Wu. “Continuum Limit
    for the Ablowitz–Ladik System.” <i>Nonlinearity</i>. IOP Publishing, 2023. <a
    href="https://doi.org/10.1088/1361-6544/acd978">https://doi.org/10.1088/1361-6544/acd978</a>.
  ieee: R. Killip, Z. Ouyang, M. Vişan, and L. Wu, “Continuum limit for the Ablowitz–Ladik
    system,” <i>Nonlinearity</i>, vol. 36, no. 7. IOP Publishing, pp. 3751–3775, 2023.
  ista: Killip R, Ouyang Z, Vişan M, Wu L. 2023. Continuum limit for the Ablowitz–Ladik
    system. Nonlinearity. 36(7), 3751–3775.
  mla: Killip, Rowan, et al. “Continuum Limit for the Ablowitz–Ladik System.” <i>Nonlinearity</i>,
    vol. 36, no. 7, IOP Publishing, 2023, pp. 3751–75, doi:<a href="https://doi.org/10.1088/1361-6544/acd978">10.1088/1361-6544/acd978</a>.
  short: R. Killip, Z. Ouyang, M. Vişan, L. Wu, Nonlinearity 36 (2023) 3751–3775.
das_tickbox: '1'
date_created: 2026-06-19T07:49:24Z
date_published: 2023-06-09T00:00:00Z
date_updated: 2026-06-25T07:54:44Z
day: '09'
doi: 10.1088/1361-6544/acd978
extern: '1'
external_id:
  arxiv:
  - '2206.02720'
intvolume: '        36'
issue: '7'
keyword:
- Ablowitz–Ladik
- continuum limit
- cubic NLS
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2206.02720
mathsc:
- 35Q55
- 37K05
- 37K10
month: '06'
oa: 1
oa_version: Preprint
page: 3751-3775
publication: Nonlinearity
publication_identifier:
  eissn:
  - 1361-6544
  issn:
  - 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Continuum limit for the Ablowitz–Ladik system
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2023'
...