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The defocusing nonlinear Schrödinger equation with t-periodic data: New exact solutions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0001-6191-7769
2015 (English)In: Nonlinear Analysis, ISSN 1468-1218, Vol. 25, 31-50 p.Article in journal (Refereed) Published
Abstract [en]

We consider solutions of the defocusing nonlinear Schrödinger (NLS) equation on the half-line whose Dirichlet and Neumann boundary values become periodic for sufficiently large t. We prove a theorem which, modulo certain assumptions, characterizes the pairs of periodic functions which can arise as Dirichlet and Neumann values for large t in this way. The theorem also provides a constructive way of determining explicit solutions with the given periodic boundary values. Hence our approach leads to a class of new exact solutions of the defocusing NLS equation on the half-line.

Place, publisher, year, edition, pages
2015. Vol. 25, 31-50 p.
Keyword [en]
Asymptotic behavior, Initial-boundary value problem, Time-periodic data, Boundary value problems, Initial value problems, Asymptotic behaviors, Explicit solutions, Initial-boundary value problems, Neumann boundary, New exact solutions, Periodic boundaries, Periodic function, Nonlinear equations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-163791DOI: 10.1016/j.nonrwa.2015.02.003Scopus ID: 2-s2.0-84925762422OAI: oai:DiVA.org:kth-163791DiVA: diva2:802402
Note

QC 20150427

Available from: 2015-04-13 Created: 2015-04-12 Last updated: 2017-12-04Bibliographically approved

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Lenells, Jonatan

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