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 αeⁱωᵗ and ceⁱωᵗ as t → ∞, respectively. Under the assumption that the initial data decay as 𝑥 → ∞, we derive necessary conditions on the parameters α, ω, c for the existence of a solution of the corresponding initial boundary value problem.