On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line

Hdl Handle:
http://hdl.handle.net/10034/560362
Title:
On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line
Authors:
Antonopoulou, Dimitra; Kamvissis, Spyridon
Abstract:
Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data su ces to make the problem well-posed but the Fokas method also requires knowledge of the values of Neumann data. The study of the Dirichlet to Neumann map is thus necessary before the application of the `Fokas transform'. In this paper, we provide a rigorous study of this map for a large class of decaying Dirichlet data. We show that the Neumann data are also su ciently decaying and that, hence, the Fokas method can be applied.
Affiliation:
Department of Mathematics, University of Chester, UK(D.A) and Department of Mathematics and Applied Mathematics, University of Crete, Greece (S.K)
Citation:
Antonopoulou, D. C. & Kamvissis, S. (2015). On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line. Nonlinearity, 28(9), 3073-3099. DOI: 10.1088/0951-7715/28/9/3073
Publisher:
IOPSCIENCE Published jointly with the London Mathematical Society
Journal:
Nonlinearity
Publication Date:
24-Jul-2015
URI:
http://hdl.handle.net/10034/560362
Additional Links:
http://iopscience.iop.org/article/10.1088/0951-7715/28/9/3073
Type:
Article
Language:
en
Description:
This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0951-7715/28/9/3073
ISSN:
0951-7715
EISSN:
1361-6544
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonopoulou, Dimitraen
dc.contributor.authorKamvissis, Spyridonen
dc.date.accessioned2015-07-14T09:54:15Zen
dc.date.available2015-07-14T09:54:15Zen
dc.date.issued2015-07-24en
dc.identifier.citationAntonopoulou, D. C. & Kamvissis, S. (2015). On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line. Nonlinearity, 28(9), 3073-3099. DOI: 10.1088/0951-7715/28/9/3073en
dc.identifier.issn0951-7715en
dc.identifier.urihttp://hdl.handle.net/10034/560362en
dc.descriptionThis is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0951-7715/28/9/3073en
dc.description.abstractInitial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data su ces to make the problem well-posed but the Fokas method also requires knowledge of the values of Neumann data. The study of the Dirichlet to Neumann map is thus necessary before the application of the `Fokas transform'. In this paper, we provide a rigorous study of this map for a large class of decaying Dirichlet data. We show that the Neumann data are also su ciently decaying and that, hence, the Fokas method can be applied.en
dc.language.isoenen
dc.publisherIOPSCIENCE Published jointly with the London Mathematical Societyen
dc.relation.urlhttp://iopscience.iop.org/article/10.1088/0951-7715/28/9/3073en
dc.titleOn the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-lineen
dc.typeArticleen
dc.identifier.eissn1361-6544en
dc.contributor.departmentDepartment of Mathematics, University of Chester, UK(D.A) and Department of Mathematics and Applied Mathematics, University of Crete, Greece (S.K)en
dc.identifier.journalNonlinearityen
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