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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, 5617-5639 p.Article 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, 5617-5639 p.
Keyword [en]
Initial-boundary value problem, Integrable system, Long-time asymptotics
National Category
URN: urn:nbn:se:kth:diva-175045DOI: 10.1016/j.jde.2015.07.003ISI: 000367755900004ScopusID: 2-s2.0-84941806505OAI: diva2:881336

QC 20151210. QC 20160203

Available from: 2015-12-10 Created: 2015-10-09 Last updated: 2016-02-03Bibliographically approved

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Lenells, Jonatan
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