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On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line
Antonopoulou, Dimitra Kamvissis, Spyridon
Antonopoulou, Dimitra
Kamvissis, Spyridon
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2015-07-24
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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.
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
IOP Publishing
Journal
Nonlinearity
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Article
Language
en
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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
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ISSN
0951-7715
EISSN
1361-6544