Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 079, 15 pages      arXiv:2003.05765      https://doi.org/10.3842/SIGMA.2020.079

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

Samuel Fromm
Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden

Received March 13, 2020, in final form August 09, 2020; Published online August 19, 2020

Abstract
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.

Key words: initial-boundary value problem; integrable system; long-time asymptotics.

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