The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane

Abstract

This work studies the initial-boundary value problem (ibvp) of the two-dimensional nonlinear Schrödinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It establishes well-posedness in the sense of Hadamard by using the explicit solution formula for the forced linear ibvp obtained via Fokas’s unified transform, and a contraction mapping argument.