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We consider solutions of the defocusing nonlinear Schr\"odinger (NLS)equation on the half-line whose Dirichlet and Neumann boundary values becomeperiodic for sufficiently large $t$. We prove a theorem which, modulo certainassumptions, characterizes the pairs of periodic functions which can arise asDirichlet and Neumann values for large $t$ in this way. The theorem alsoprovides a constructive way of determining explicit solutions with the givenperiodic boundary values. Hence our approach leads to a class of new exactsolutions of the defocusing NLS equation on the half-line.

The defocusing nonlinear Schr\"odinger equation with $t$-periodic data: New exact solutions