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On asymptotic stability of solitary waves for nonlinear Schrödinger equations

✍ Scribed by Vladimir S. Buslaev; Catherine Sulem

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
401 KB
Volume
20
Category
Article
ISSN
0294-1449

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✦ Synopsis

We study the long-time behavior of solutions of the nonlinear Schrödinger 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 Schrödinger equation. We explicitly calculate the time behavior of the correction.

📜 SIMILAR VOLUMES

Orbital Stability of Solitary Waves for
Orbital Stability of Solitary Waves for the Nonlinear Derivative Schrödinger Equation
✍ B.L. Guo; Y.P. Wu 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 445 KB

Consider herein are the stability of the solitary waves \(e^{-i \omega u s} e^{i \psi(x-t t)} a(x-v t)\) for the following nonlinear quintic derivative Schrödinger equation. \[ u_{t}=i u_{x x}+i\left(c_{3}|u|^{2}+c_{s}|u|^{4}\right) u+\left[\left(s_{0}+s_{2}|u|^{2}\right) u\right]_{v}, \quad u \in