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