The nonlinear Schrödinger equation on the half-line with homogeneous Robin boundary conditions.

We consider the nonlinear Schrödinger equation on the half-line with a Robin boundary condition at and with initial data in the weighted Sobolev space . We prove that there exists a global weak solution of this initial-boundary value problem and provide a representation for the solution in terms of the solution of a Riemann-Hilbert problem. Using this representation, we obtain asymptotic formulas for the long-time behavior of the solution.