On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line
AffiliationDepartment of Mathematics, University of Chester, UK(D.A) and Department of Mathematics and Applied Mathematics, University of Crete, Greece (S.K)
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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.
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: 10.1088/0951-7715/28/9/3073
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/10.1088/0951-7715/28/9/3073
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