Stability of KAM Tori for Nonlinear Schrodinger Equation

Hongzi Cong, Jianjun Liu, Xiaoping Yuan (Autoren)

Buch | Softcover

85 Seiten

2016
American Mathematical Society (Verlag)
978-1-4704-1657-7 (ISBN)

Titel z.Zt. nicht lieferbar
Versandkostenfrei
Auch auf Rechnung

Artikel merken

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 $/varepsilon/rightarrow0$.

Hongzi Cong, Dalian University of Technology, China. Jianjun Liu, Sichuan University, Chengdu, Sichuan, China. Xiaoping Yuan, Fudan University, Shanghai, China.

Introduction and main results
Some notations and the abstract results
Properties of the Hamiltonian with $p$-tame property
Proof of Theorem 2.9 and Theorem 2.10
Proof of Theorem 2.11
Proof of Theorem 1.1
Appendix: technical lemmas
Bibliography
Index

Erscheinungsdatum	01.03.2016
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	187 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-1657-3 / 1470416573
ISBN-13	978-1-4704-1657-7 / 9781470416577
Zustand	Neuware