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- W4288555239 abstract "In this paper, we study the following nonlinear Schrodinger equation begin{eqnarray}label{maineq0} textbf{i}u_{t}-u_{xx}+V*u+epsilon f(x)|u|^4u=0, xinmathbb{T}=mathbb{R}/2pimathbb{Z}, end{eqnarray} where $V*$ is the Fourier multiplier defined by $widehat{(V* u})_n=V_{n}widehat{u}_n, V_nin[-1,1]$ and $f(x)$ is Gevrey smooth. It is shown that for $0leq|epsilon|ll1$, there is some $(V_n)_{ninmathbb{Z}}$ such that, the equation admits a time almost periodic solution (i.e., full dimensional KAM torus) in the Gevrey space. This extends results of Bourgain cite{BJFA2005} and Cong-Liu-Shi-Yuan cite{CLSY} to the case that the nonlinear perturbation depends explicitly on the space variable $x$. The main difficulty here is the absence of zero momentum of the equation." @default.
- W4288555239 created "2022-07-29" @default.
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- W4288555239 date "2019-02-28" @default.
- W4288555239 modified "2023-10-16" @default.
- W4288555239 title "On the existence of full dimensional KAM torus for nonlinear Schrodinger equation" @default.
- W4288555239 doi "https://doi.org/10.48550/arxiv.1903.00127" @default.
- W4288555239 hasPublicationYear "2019" @default.
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