Admissible boundary values for the Gerdjikov-Ivanov equation with asymptotically time-periodic boundary data

Samuel Fromm

Published 2020-03-12Version 1

We consider the Gerdjikov-Ivanov equation in the quarter plane with Dirichlet boundary data and Neumann value converging to single exponentials $\alpha e^{i\omega t}$ and $ce^{i\omega t}$ 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.