Addendum to 'On the Dirichlet to Neumann problem for the 1-dimensional cubic NLS equation on the half-line'. (31st August 2016)

• Record Type: Journal Article
• Authors: Antonopoulou, D C; Kamvissis, S
• Is Part Of: Nonlinearity. Volume 29:Number 10(2016:Oct.)
• Page Start: 3206
• Page End: 3214
• Publication Date: 2016-08-31
• Subjects: Fokas unified method -- NLS -- Dirichlet to Neumann; 35Q51 -- 35Q55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/10/3206
• Languages: English
• ISSNs: 0951-7715

Abstract

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.