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Stability of KAM tori for nonlinear Schrödinger equation by Hongzi Cong, Jianjun Liu and Xiaoping Yuan is a nonfiction available to read on EtoBox.

What is Stability of KAM tori for nonlinear Schrödinger equation about?

The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger 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 $\varepsilon\rightarrow0$.

Who reads Stability of KAM tori for nonlinear Schrödinger equation?

Author

Hongzi Cong, Jianjun Liu and Xiaoping Yuan

Publisher

American Mathematical Society

Published

2016

Language

EN

ISBN

9781470416577

Category

nonfiction

Subjects

Computer Science, Science, Mathematics