Admissible Boundary Values for the Gerdjikov–Ivanov Equation with Asymptotically Time-Periodic Boundary Data

We consider the Gerdjikov–Ivanov equation in the quarter plane with Dirichlet boundary data and Neumann value converging to single exponentials $\alpha \mathrm{e}^{{\rm i}\omega t}$ and $c\mathrm{e}^{\mathrm{i}\omega t}$ as $t\to\infty$, respectively. Under the assumption that the initial data decay as $x\to\infty$, we derive necessary conditions on the parameters $\alpha$, $\omega$, $c$ for the existence of a solution of the corresponding initial boundary value problem.