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 $\alpha {\rm e}^{{\rm i}\omega t}$and$c{\rm e}^{{\rm i}\omega t}$as$t\to\infty$, respectively. Under the assumption that the initial data decay as $x\to \mathrm{\infty }$, we derive necessary conditions on the parameters $\alpha$, $\omega$, $c$ for the existence of a solution of the corresponding initial boundary value problem.