Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data
| Autor: | Percy Deift, Jungwoon Park |
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| Rok vydání: | 2011 |
| Předmět: |
General Mathematics
010102 general mathematics Boundary problem Mathematical analysis Mathematics::Analysis of PDEs Perturbation (astronomy) 01 natural sciences Robin boundary condition 010305 fluids & plasmas Nonlinear system Mathematics - Analysis of PDEs Nonlinear Sciences::Exactly Solvable and Integrable Systems Transformation (function) Exponential stability 0103 physical sciences Line (geometry) FOS: Mathematics 0101 mathematics Nonlinear Sciences::Pattern Formation and Solitons Delta potential Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | International Mathematics Research Notices. |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnq282 |
| Popis: | We consider the one-dimensional focusing nonlinear Schr\"odinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a B\"acklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, earlier work on the problem by Holmer and Zworski. |
| Databáze: | OpenAIRE |
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