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The initial-boundary value problem (IBVP) for the nonlinear Schr\"odinger(NLS) equation on the half-plane with nonzero boundary data is studied byadvancing a novel approach recently developed for the well-posedness of thecubic NLS on the half-line, which takes advantage of the solution formulaproduced by the unified transform of Fokas for the associated linear IBVP. Forinitial data in Sobolev spaces on the half-plane and boundary data in Bourgainspaces arising naturally when the linear IBVP is solved with zero initial data,the present work provides a local well-posedness result for NLSinitial-boundary value problems in higher dimensions.

Well-Posedness of the Nonlinear Schr\"odinger Equation on the Half-Plane