Stability of KAM tori for nonlinear Schrödinger equation. Memoirs of the American Mathematical Society; Bd. volume 239, number 1134 (6th of 6 numbers).

Cong, Hongzi; Liu, Jianjun; Yuan, Xiaoping

ISBN 10: 1470416573 / ISBN 13: 9781470416577

Edité par Providence, American Mathematical Society, 2016

A propos de cet article

Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03394 9781470416577 Sprache: Englisch Gewicht in Gramm: 150.

N° de réf. du vendeur 2489302

Détails bibliographiques

• Titre: Stability of KAM tori for nonlinear Schrödinger equation. Memoirs of the American Mathematical Society; Bd. volume 239, number 1134 (6th of 6 numbers).
• Éditeur: Providence, American Mathematical Society
• Date de parution: 2016
• Langue: anglais
• ISBN à 10 chiffres: 1470416573
• ISBN à 13 chiffres: 9781470416577
• Reliure: Softcover
• Poids: 150 grammes
• Catalogues du vendeur:
  • SA MATHEMATIK

A propos de ce titre

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 $\varepsilon\rightarrow0$.

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.