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

Published by Providence, American Mathematical Society, 2016

About this Item

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

Seller Inventory # 2489302

Bibliographic Details

• Title: Stability of KAM tori for nonlinear Schrödinger equation. Memoirs of the American Mathematical Society; Bd. volume 239, number 1134 (6th of 6 numbers).
• Publisher: Providence, American Mathematical Society
• Publication Date: 2016
• Language: English
• ISBN 10: 1470416573
• ISBN 13: 9781470416577
• Binding: Softcover
• Weight: 150 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

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 $\varepsilon\rightarrow0$.

About the Author

Hongzi Cong, Dalian University of Technology, China.

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

Xiaoping Yuan, Fudan University, Shanghai, China.