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

Symmetry Integrability and Geometry-Methods and Applications

article

Samuel Fromm¹ 

[1] Department of Mathematics, KTH Royal Institute of Technology

关键词: initial-boundary value problem;    integrable system;    long-time asymptotics 2020 Mathematics Subject Classification 37K15;    35Q15;   

DOI  :  10.3842/SIGMA.2020.079

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown