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

Abstract

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

References in corpus (2)

• The derivative nonlinear Schrödinger equation on the half-line
• On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS equation on the Half-Line; Zero Initial Data

Cited by in corpus (1)

• The long-time asymptotic of the derivative nonlinear Schr$\ddot{o}$dinger equation with step-like initial value