The nonlinear Schrodinger equation on the half-line with Neumann boundary conditions

摘要

The initial-boundary value problem on the half-line for the nonlinear Schrodinger equation supplemented with a Neumann boundary condition is shown to be locally well-posed in the sense of Hadamard for data in Sobolev spaces H-S. The proof takes advantage of a novel explicit solution formula for the forced linear counterpart of the nonlinear problem, which is obtained via Fokas' unified transform method. This formula provides the basis for setting up a Picard iteration scheme and for deriving the linear estimates required for proving local well-posedness of the nonlinear problem via a contraction mapping argument. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.