---
OA_place: repository
OA_type: green
_id: '22071'
abstract:
- lang: eng
  text: "We consider the cubic–quintic nonlinear Schrödinger equation: (mathematical
    formular)\r\nIn the first part of the paper, we analyze the one-parameter family
    of ground state solitons associated to this equation with particular attention
    to the shape of the associated mass/energy curve. Additionally, we are able to
    characterize the kernel of the linearized operator about such solitons and to
    demonstrate that they occur as optimizers for a one-parameter family of inequalities
    of Gagliardo–Nirenberg type. Building on this work, in the latter part of the
    paper we prove that scattering holds for solutions belonging to the region R of
    the mass/energy plane where the virial is positive. We show that this region is
    partially bounded by solitons also by rescalings of solitons (which are not soliton
    solutions in their own right). The discovery of rescaled solitons in this context
    is new and highlights an unexpected limitation of any virial-based methodology."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Tadahiro
  full_name: Oh, Tadahiro
  last_name: Oh
- first_name: Oana
  full_name: Pocovnicu, Oana
  last_name: Pocovnicu
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Oh T, Pocovnicu O, Vişan M. Solitons and scattering for the cubic-quintic
    nonlinear Schrödinger equation on R^3. <i>Archive for Rational Mechanics and Analysis</i>.
    2017;225:469-548. doi:<a href="https://doi.org/10.1007/s00205-017-1109-0">10.1007/s00205-017-1109-0</a>
  apa: Killip, R., Oh, T., Pocovnicu, O., &#38; Vişan, M. (2017). Solitons and scattering
    for the cubic-quintic nonlinear Schrödinger equation on R^3. <i>Archive for Rational
    Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-017-1109-0">https://doi.org/10.1007/s00205-017-1109-0</a>
  chicago: Killip, Rowan, Tadahiro Oh, Oana Pocovnicu, and Monica Vişan. “Solitons
    and Scattering for the Cubic-Quintic Nonlinear Schrödinger Equation on R^3.” <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature, 2017. <a href="https://doi.org/10.1007/s00205-017-1109-0">https://doi.org/10.1007/s00205-017-1109-0</a>.
  ieee: R. Killip, T. Oh, O. Pocovnicu, and M. Vişan, “Solitons and scattering for
    the cubic-quintic nonlinear Schrödinger equation on R^3,” <i>Archive for Rational
    Mechanics and Analysis</i>, vol. 225. Springer Nature, pp. 469–548, 2017.
  ista: Killip R, Oh T, Pocovnicu O, Vişan M. 2017. Solitons and scattering for the
    cubic-quintic nonlinear Schrödinger equation on R^3. Archive for Rational Mechanics
    and Analysis. 225, 469–548.
  mla: Killip, Rowan, et al. “Solitons and Scattering for the Cubic-Quintic Nonlinear
    Schrödinger Equation on R^3.” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 225, Springer Nature, 2017, pp. 469–548, doi:<a href="https://doi.org/10.1007/s00205-017-1109-0">10.1007/s00205-017-1109-0</a>.
  short: R. Killip, T. Oh, O. Pocovnicu, M. Vişan, Archive for Rational Mechanics
    and Analysis 225 (2017) 469–548.
date_created: 2026-06-19T08:21:38Z
date_published: 2017-07-01T00:00:00Z
date_updated: 2026-06-30T10:52:12Z
day: '01'
doi: 10.1007/s00205-017-1109-0
extern: '1'
external_id:
  arxiv:
  - '1409.6734'
intvolume: '       225'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1409.6734
month: '07'
oa: 1
oa_version: Preprint
page: 469-548
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation
  on R^3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 225
year: '2017'
...