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