Admissible boundary values for the defocusing nonlinear Schrodinger equation with asymptotically time-periodic data

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Lenells, Jonatan¹ 

[1] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

关键词: Initial-boundary value problem;    Integrable system;    Long-time asymptotics;   

DOI  :  10.1016/j.jde.2015.07.003

来源: Elsevier

【 摘 要 】

We consider solutions of the defocusing nonlinear Schrodinger equation in the quarter plane whose Dirichlet boundary data approach a single exponential alpha(ei omega t) as t ->infinity. In order to determine the long time asymptotics of the solution, it is necessary to first characterize the asymptotic behavior of the Neumann value in terms of the given data. Assuming that the initial data decay as x ->infinity, we derive necessary conditions for the Neumann value to asymptote towards a single exponential of the form ce(i omega t). Since our approach yields expressions which relate alpha, omega, and c, the result can be viewed as a characterization of the large t behavior of the Dirichlet to Neumann map for single exponential profiles. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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