On the Dirichlet to Neumann problem for the 1-dimensional cubic NLS equation on the half-line

• Published in: Nonlinearity Vol. 28; no. 9; pp. 3073 - 3099
• Main Authors: Antonopoulou, D C, Kamvissis, S
• Format: Journal Article
• Language: English
• Published: 01.09.2015
• Subjects: Boundary value problems; Decay; Dirichlet problem; Initial value problems; Mathematical analysis; Nonlinearity; Transforms; Well posed problems

Initial-boundary value problems for one-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 giv...