Addendum to 'On the Dirichlet to Neumann problem for the 1-dimensional cubic NLS equation on the half-line'. (31st August 2016) - Antonopoulou, D C; Kamvissis, S
Abstract: We present a short note on the extension of the results of Antonopoulou and Kamvissis 2015 Nonlinearity 28 3073–99 to the case of non-zero initial data. More specifically, the defocusing cubic NLS equation is considered on the half-line with decaying (in time) Dirichlet data and sufficiently smooth and decaying (in space) initial data. We prove that for this case also, and for a large class of decaying Dirichlet data, the Neumann data are sufficiently decaying so that the Fokas unified method for the solution of defocusing NLS is applicable.