---
OA_place: repository
OA_type: green
_id: '22045'
abstract:
- lang: eng
  text: "We consider the initial-value problem for the cubic-quintic nonlinear Schrödinger
    equation (\U0001D456\U0001D715\U0001D461+Δ)⁢\U0001D713 =\U0001D6FC1⁢\U0001D713
    −\U0001D6FC3⁢|\U0001D713|2⁢\U0001D713 +\U0001D6FC5⁢|\U0001D713|4⁢\U0001D713 in
    three spatial dimensions in the class of solutions with |\U0001D713⁡(\U0001D465)|
    →\U0001D450 >0 as |\U0001D465| →∞. Here \U0001D6FC1, \U0001D6FC3, \U0001D6FC5,
    and \U0001D450 are such that \U0001D713⁡(\U0001D465) ≡\U0001D450 is an energetically
    stable equilibrium solution to this equation. Normalizing the boundary condition
    to \U0001D713⁡(\U0001D465) →1 as |\U0001D465| →∞, we study the associated initial-value
    problem for \U0001D462 =\U0001D713 −1 and prove a scattering result for small
    initial data in a weighted Sobolev space."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Jason
  full_name: Murphy, Jason
  last_name: Murphy
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Murphy J, Vişan M. The initial-value problem for the cubic-quintic
    NLS with nonvanishing boundary conditions. <i>SIAM Journal on Mathematical Analysis</i>.
    2018;50(3):2681-2739. doi:<a href="https://doi.org/10.1137/17m1116702">10.1137/17m1116702</a>
  apa: Killip, R., Murphy, J., &#38; Vişan, M. (2018). The initial-value problem for
    the cubic-quintic NLS with nonvanishing boundary conditions. <i>SIAM Journal on
    Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics. <a
    href="https://doi.org/10.1137/17m1116702">https://doi.org/10.1137/17m1116702</a>
  chicago: Killip, Rowan, Jason Murphy, and Monica Vişan. “The Initial-Value Problem
    for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>SIAM Journal
    on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics,
    2018. <a href="https://doi.org/10.1137/17m1116702">https://doi.org/10.1137/17m1116702</a>.
  ieee: R. Killip, J. Murphy, and M. Vişan, “The initial-value problem for the cubic-quintic
    NLS with nonvanishing boundary conditions,” <i>SIAM Journal on Mathematical Analysis</i>,
    vol. 50, no. 3. Society for Industrial &#38; Applied Mathematics, pp. 2681–2739,
    2018.
  ista: Killip R, Murphy J, Vişan M. 2018. The initial-value problem for the cubic-quintic
    NLS with nonvanishing boundary conditions. SIAM Journal on Mathematical Analysis.
    50(3), 2681–2739.
  mla: Killip, Rowan, et al. “The Initial-Value Problem for the Cubic-Quintic NLS
    with Nonvanishing Boundary Conditions.” <i>SIAM Journal on Mathematical Analysis</i>,
    vol. 50, no. 3, Society for Industrial &#38; Applied Mathematics, 2018, pp. 2681–739,
    doi:<a href="https://doi.org/10.1137/17m1116702">10.1137/17m1116702</a>.
  short: R. Killip, J. Murphy, M. Vişan, SIAM Journal on Mathematical Analysis 50
    (2018) 2681–2739.
das_tickbox: '1'
date_created: 2026-06-19T07:49:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2026-06-25T07:49:21Z
day: '01'
doi: 10.1137/17m1116702
extern: '1'
external_id:
  arxiv:
  - '1702.04413'
intvolume: '        50'
issue: '3'
keyword:
- cubic-quintic NLS
- nonvanishing boundary conditions
- space-time resonances
- scattering
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1702.04413
mathsc:
- 35Q55
month: '01'
oa: 1
oa_version: Preprint
page: 2681-2739
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
  issn:
  - 0036-1410
  - 1095-7154
publication_status: published
publisher: Society for Industrial & Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The initial-value problem for the cubic-quintic NLS with nonvanishing boundary
  conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2018'
...