Stability of KAM Tori for Nonlinear Schroedinger Equation PDF
by Hongzi Cong
Description
The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schroedinger equation $\sqrt{-1}\, u_{t}=u_{xx}-M_{\xi}u+\varepsilonu^2u,$ 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 $\varepsilon\rightarrow0$.
Information
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Download - Immediately Available
- Format:PDF
- Pages:85 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470427511
Information
-
Download - Immediately Available
- Format:PDF
- Pages:85 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470427511
