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Admissible boundary values for the Gerdjikov-Ivanov equation with asymptotically time-periodic boundary data. (English) Zbl 1458.37072

Summary: 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.

MSC:

37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q15 Riemann-Hilbert problems in context of PDEs
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