On asymptotic stability of solitary waves for nonlinear Schrödinger equations
| Autor: | Vladimir Buslaev, Catherine Sulem |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Partial differential equation
Applied Mathematics Mathematical analysis Eigenfunction Schrödinger equation symbols.namesake Nonlinear system symbols Riccati equation Initial value problem Soliton Nonlinear Sciences::Pattern Formation and Solitons Nonlinear Schrödinger equation Mathematical Physics Analysis Mathematics |
| Zdroj: | Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 20:419-475 |
| ISSN: | 1873-1430 0294-1449 |
| Popis: | We study the long-time behavior of solutions of the nonlinear Schrodinger equation in one space dimension for initial conditions in a small neighborhood of a stable solitary wave. Under some hypothesis on the structure of the spectrum of the linearized operator, we prove that, asymptotically in time, the solution decomposes into a solitary wave with slightly modified parameters and a dispersive part described by the free Schrodinger equation. We explicitly calculate the time behavior of the correction. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|