Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Admissible boundary values for the defocusing nonlinear Schrödinger equation with asymptotically time-periodic data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6191-7769
2015 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 11, p. 5617-5639Article in journal (Refereed) Published
Abstract [en]

We consider solutions of the defocusing nonlinear Schrödinger equation in the quarter plane whose Dirichlet boundary data approach a single exponential αeiωt as t→∞. In order to determine the long time asymptotics of the solution, it is necessary to first characterize the asymptotic behavior of the Neumann value in terms of the given data. Assuming that the initial data decay as x→∞, we derive necessary conditions for the Neumann value to asymptote towards a single exponential of the form ceiωt. Since our approach yields expressions which relate α, ω, and c, the result can be viewed as a characterization of the large t behavior of the Dirichlet to Neumann map for single exponential profiles.

Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 259, no 11, p. 5617-5639
Keywords [en]
Initial-boundary value problem, Integrable system, Long-time asymptotics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-175045DOI: 10.1016/j.jde.2015.07.003ISI: 000367755900004Scopus ID: 2-s2.0-84941806505OAI: oai:DiVA.org:kth-175045DiVA, id: diva2:881336
Note

QC 20151210. QC 20160203

Available from: 2015-12-10 Created: 2015-10-09 Last updated: 2017-12-01Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Lenells, Jonatan

Search in DiVA

By author/editor
Lenells, Jonatan
By organisation
Mathematics (Div.)
In the same journal
Journal of Differential Equations
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 31 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf