Orbital Stability of Solitary Waves for the Nonlinear Derivative Schrödinger Equation

✍ Scribed by B.L. Guo; Y.P. Wu

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 445 KB
• Volume: 123
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1995.1156

✦ Synopsis

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 R
]

For the case (s_{2} \neq 0), the abstract results of Grillakis et al. ([5,6]) do not apply directly. By constructing three appropriate invariants of motion and detailed spectral analysis, we obtain the stability of the solitary waves. 1995 Academic Press. Ine.