Construction of solutions of the defocusing nonlinear Schr"odinger equation with asymptotically time-periodic boundary values

We study the defocusing nonlinear Schrodinger equation in the quarter plane with asymptotically periodic boundary values. We use the unified transform method, also known as the Fokas method, and the Deift-Zhou nonlinear steepest descent method to construct solutions in a sector close to the boundary whose leading behavior is described by a single exponential plane wave. Furthermore, we compute the subleading terms in the long-time asymptotics of the constructed solutions.