Solitary waves for a class of quasilinear Schrödinger equations in dimension two
✍ Scribed by João Marcos do Ó; Uberlandio Severo
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 452 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0944-2669
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📜 SIMILAR VOLUMES
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
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