---
OA_place: repository
OA_type: green
_id: '22027'
abstract:
- lang: eng
  text: We demonstrate that in three space dimensions, the scattering behaviour of
    semilinear wave equations with quintic-type nonlinearities uniquely determines
    the nonlinearity. The nonlinearity is permitted to depend on both space and time.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicholas
  full_name: Hu, Nicholas
  last_name: Hu
- 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: Hu N, Killip R, Vişan M. Deconvolutional determination of the nonlinearity
    in a semilinear wave equation. <i>Pure and Applied Analysis</i>. 2025;7(1):1-17.
    doi:<a href="https://doi.org/10.2140/paa.2025.7.1">10.2140/paa.2025.7.1</a>
  apa: Hu, N., Killip, R., &#38; Vişan, M. (2025). Deconvolutional determination of
    the nonlinearity in a semilinear wave equation. <i>Pure and Applied Analysis</i>.
    Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/paa.2025.7.1">https://doi.org/10.2140/paa.2025.7.1</a>
  chicago: Hu, Nicholas, Rowan Killip, and Monica Vişan. “Deconvolutional Determination
    of the Nonlinearity in a Semilinear Wave Equation.” <i>Pure and Applied Analysis</i>.
    Mathematical Sciences Publishers, 2025. <a href="https://doi.org/10.2140/paa.2025.7.1">https://doi.org/10.2140/paa.2025.7.1</a>.
  ieee: N. Hu, R. Killip, and M. Vişan, “Deconvolutional determination of the nonlinearity
    in a semilinear wave equation,” <i>Pure and Applied Analysis</i>, vol. 7, no.
    1. Mathematical Sciences Publishers, pp. 1–17, 2025.
  ista: Hu N, Killip R, Vişan M. 2025. Deconvolutional determination of the nonlinearity
    in a semilinear wave equation. Pure and Applied Analysis. 7(1), 1–17.
  mla: Hu, Nicholas, et al. “Deconvolutional Determination of the Nonlinearity in
    a Semilinear Wave Equation.” <i>Pure and Applied Analysis</i>, vol. 7, no. 1,
    Mathematical Sciences Publishers, 2025, pp. 1–17, doi:<a href="https://doi.org/10.2140/paa.2025.7.1">10.2140/paa.2025.7.1</a>.
  short: N. Hu, R. Killip, M. Vişan, Pure and Applied Analysis 7 (2025) 1–17.
das_tickbox: '1'
date_created: 2026-06-19T07:36:00Z
date_published: 2025-01-22T00:00:00Z
date_updated: 2026-06-22T10:35:34Z
day: '22'
doi: 10.2140/paa.2025.7.1
extern: '1'
external_id:
  arxiv:
  - '2307.00829'
intvolume: '         7'
issue: '1'
keyword:
- dispersive equations
- nonlinear wave equation
- semilinear wave equation
- scattering
- inverse scattering
- deconvolution
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2307.00829
month: '01'
oa: 1
oa_version: Preprint
page: 1-17
publication: Pure and Applied Analysis
publication_identifier:
  eissn:
  - 2578-5885
  issn:
  - 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Deconvolutional determination of the nonlinearity in a semilinear wave equation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2025'
...