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The most challenging problem in the implementation of the so-called unified transform to the NLS on the half line, is the characterisation of the unknown boundary value in terms of the given data. First, an effective perturbative method will be presented for the asymptotic computation of the Neumann boundary value for given t-periodic Dirichlet data. Then, certain analytical results will be discussed, extending the relevant pioneering results of A. Boutet de Monvel and collaborators. |
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