Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417083 | Journal of Differential Equations | 2015 | 23 Pages |
Abstract
We consider solutions of the defocusing nonlinear Schrödinger equation in the quarter plane whose Dirichlet boundary data approach a single exponential αeiÏt as tââ. 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 xââ, we derive necessary conditions for the Neumann value to asymptote towards a single exponential of the form ceiÏt. Since our approach yields expressions which relate α, Ï, 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jonatan Lenells,