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- W3176265571 abstract "In this paper, we prove the existence of full dimensional tori for $d$-dimensional nonlinear Schr$ddot{mbox{o}}$dinger equation with periodic boundary conditions begin{equation*}label{L1} sqrt{-1}u_{t}+Delta u+V*upmepsilon |u|^2u=0,hspace{12pt}xinmathbb{T}^d,quad dgeq 1, end{equation*} where $V*$ is the convolution potential. Here the radius of the invariant torus satisfies a slower decay, i.e. begin{equation*}label{031601} I_{textbf n}sim e^{-rln^{sigma}left|textbf nright|},qquad mbox{as} left|textbf nright|rightarrowinfty, end{equation*}for any $sigma>2$ and $rgeq 1$. This result confirms a conjecture by Bourgain [J. Funct. Anal. 229 (2005), no. 1, 62-94]." @default.
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- W3176265571 date "2021-06-24" @default.
- W3176265571 modified "2023-10-16" @default.
- W3176265571 title "The Existence of full dimensional tori for d-dimensional Nonlinear Schr$ddot{mbox{O}}$dinger equation" @default.
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