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Stability of KAM Tori for Nonlinear Schrodinger Equation (Memoirs of the American Mathematical Society)

Differential Equations

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About the Author Hongzi Cong, Dalian University of Technology, China.Jianjun Liu, Sichuan University, Chengdu, Sichuan, China.Xiaoping Yuan, Fudan University, Shanghai, China. Product 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 $\varepsilon\rightarrow0$.

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Format: paperback
ASIN: 1470416573
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Differential Equations
Domain: Amazon UK
Release Date: 30 January 2016
Listed Since: 15 October 2015

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Stability of KAM Tori for Nonlinear Schrodinger Equation (Memoirs of the American Mathematical Society)

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