The defocusing nonlinear Schrödinger equation with tt-periodic data: New exact solutions

We consider solutions of the defocusing nonlinear Schrödinger (NLS) equation on the half-line whose Dirichlet and Neumann boundary values become periodic for sufficiently large tt. We prove a theorem which, modulo certain assumptions, characterizes the pairs of periodic functions which can arise as Dirichlet and Neumann values for large tt in this way. The theorem also provides a constructive way of determining explicit solutions with the given periodic boundary values. Hence our approach leads to a class of new exact solutions of the defocusing NLS equation on the half-line.