Stability of KAM Tori for Nonlinear Schrodinger Equation Paperback / softback
by Hongzi Cong, Jianjun Liu, Xiaoping Yuan
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
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 $\varepsilon\rightarrow0$.
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:85 pages
- Publisher:American Mathematical Society
- Publication Date:30/01/2016
- Category:
- ISBN:9781470416577
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:85 pages
- Publisher:American Mathematical Society
- Publication Date:30/01/2016
- Category:
- ISBN:9781470416577
