Stability of Kam Tori for Nonlinear Schrodinger Equation - Couverture souple

Cong, Hongzi; Liu, Jianjun; Yuan, Xiaoping

Couverture souple

ISBN 10 : 1470416573 ISBN 13 : 9781470416577

Editeur : American Mathematical Society, 2016

Synopsis

The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrodinger equation $$\sqrt{-1}\, u_{t}=u_{xx}-M_{\xi}u+\varepsilon|u|^2u,$$ subject to Dirichlet boundary conditions $u(t,0)=u(t,\pi)=0$, where $M_{\xi}$ is a real Fourier multiplier. More precisely, they show that, for a typical Fourier multiplier $M_{\xi}$, any solution with the initial datum in the $\delta$-neighborhood of a KAM torus still stays in the $2\delta$-neighborhood of the KAM torus for a polynomial long time such as $|t|\leq \delta^{-\mathcal{M}}$ for any given $\mathcal M$ with $0\leq \mathcal{M}\leq C(\varepsilon)$, where $C(\varepsilon)$ is a constant depending on $\varepsilon$ and $C(\varepsilon)\rightarrow\infty$ as $\varepsilon\rightarrow0$.

A propos du livre

À propos de l?auteur

Hongzi Cong, Dalian University of Technology, China.

Jianjun Liu, Sichuan University, Chengdu, Sichuan, China.

Xiaoping Yuan, Fudan University, Shanghai, China.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 1470416573
• ISBN 13: 9781470416577
• Reliure: Broché
• Nombre de pages: 85
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible