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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
Abstract:
We consider the Gerdjikov–Ivanov equation in the quarter plane with Dirichlet boundary data and Neumann value converging to single exponentials $\alpha \mathrm{e}^{{\rm i}\omega t}$ 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.
Keywords:
initial-boundary value problem, integrable system, long-time asymptotics.
Received: March 13, 2020; in final form August 9, 2020; Published online August 19, 2020
Citation:
Samuel Fromm, “Admissible Boundary Values for the Gerdjikov–Ivanov Equation with Asymptotically Time-Periodic Boundary Data”, SIGMA, 16 (2020), 079, 15 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1616 https://www.mathnet.ru/eng/sigma/v16/p79
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Abstract page: | 69 | Full-text PDF : | 13 | References: | 14 |
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