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

This work studies the initial-boundary value problem 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 utilizing the explicit solution formula for the forced linear initial-boundary value problem obtained via Fokas's unified transform, and a contraction mapping argument.

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