## Communicated by B. Brosowski This paper concerns the orbital stability for solitary waves of the ¸ong ¼ave-Short ¼ave resonance equations. Since the abstract results of Grillakis et al. [7,8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral a
Orbital Stability of Solitary Wave Solutions for an Interaction Equation of Short and Long Dispersive Waves
✍ Scribed by Jaime Angulo Pava; José Fabio B. Montenegro
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 169 KB
- Volume
- 174
- Category
- Article
- ISSN
- 0022-0396
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## dedicated to professor rentaro agemi on his sixtieth birthday We show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction It is shown that for any initial data (u 0 , v 0 ) # H s (R)\_H s&1Â2 (R) (s 0), the solution for the above equation
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