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

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