Admissible boundary values for the defocusing nonlinear Schr "odinger\n equation with asymptotically time-periodic data

2014/07/18 by Jonatan Lenells, Lenells, Jonatan
Engineering · Mathematics · Physics and Astronomy · #35Q15 #37K15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1407.5046

openalex publication_date 2014/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider solutions of the defocusing nonlinear Schr "odinger equation in\nthe quarter plane whose Dirichlet boundary data approach a single exponential\n\α e^{i\ω t} as t \→ \∞. In order to determine the long time\nasymptotics of the solution, it is necessary to first characterize the\nasymptotic behavior of the Neumann value in terms of the given data. Assuming\nthat the initial data decay as x \→ \∞, we derive necessary conditions\nfor the Neumann value to asymptote towards a single exponential of the form\nce^{i\ω t}. Since our approach yields expressions which relate \α,\n\ω, and c, the result can be viewed as a characterization of the large\nt behavior of the Dirichlet to Neumann map for single exponential profiles.\n

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