#### How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

2. Complete and sign the license agreement.

3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

# memo_has_moved_text();Stability of KAM tori for nonlinear Schrödinger equation

Hongzi Cong, Jianjun Liu and Xiaoping Yuan

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 239, Number 1134
ISBNs: 978-1-4704-1657-7 (print); 978-1-4704-2751-1 (online)
DOI: http://dx.doi.org/10.1090/memo/1134
Published electronically: July 27, 2015
Keywords:KAM tori, Normal form, Stability, $p$-tame property

View full volume PDF

View other years and numbers:

Chapters

• Preface
• Chapter 1. Introduction and main results
• Chapter 2. Some notations and the abstract results
• Chapter 3. Properties of the Hamiltonian with $p$-tame property
• Chapter 4. Proof of Theorem 2.9 and Theorem 2.10
• Chapter 5. Proof of Theorem 2.11
• Chapter 6. Proof of Theorem 1.1
• Chapter 7. Appendix: technical lemmas

### Abstract

We prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation

subject to Dirichlet boundary conditions $u(t,0)=u(t,\pi )=0$, where $M_{\xi }$ is a real Fourier multiplier. More precisely, we 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 $\varepsilon \rightarrow 0$.