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 $x\to\infty$, we derive necessary conditions on the parameters $\alpha$, $\omega$, $c$ for the existence of a solution of the corresponding initial boundary value problem.
Categories: math.AP