We prove, by adapting the method of Colliander-Kenig [9], local well posedness of the initial-boundary-value problem for the one-dimensional nonlinear Schrödinger equation i∂ₜu +∂ₓ²u +λ u|u|α-1=0 on the half-line under low boundary regularity assumptions.
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Justin Holmer (2005) studied this question.
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