### All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
 On the existence of full dimensional KAM torus for fractional nonlinear Schr\"odinger equation. Yuan Wu,Xiaoping Yuan Keywords:KAM theory, Almost periodic solution, Gevrey space, Fractional nonlinear Schr\"odinger equation. Abstract: In this paper,\ we study fractional nonlinear Schr\"{o}dinger equation (FNLS) with periodic boundary condition \begin{eqnarray}\label{maineq0} \textbf{i}u_{t}=-(-\Delta)^{s_{0}} u-V*u-\epsilon f(x)|u|^4u,\ ~~x\in \mathbb{T}, ~~t\in \mathbb{R}, ~~s_{0}\in (\frac12,1), \end{eqnarray} where $(-\Delta)^{s_{0}}$ is the Riesz fractional differentiation defined in \cite{ki2006th} and $V*$ is the Fourier multiplier defined by \begin{equation*}\widehat{V*u}(n)=V_n\widehat{u}(n),\ V_n\in\left[-1,1\right], \end{equation*} and $f(x)$ is Gevrey smooth.\ We prove that for $0\leq|\epsilon|\ll1$ and appropriate $V$,\ the equation (\ref{maineq0}) admits a full dimensional KAM torus in the Gevrey space satisfying \begin{equation*} \frac12e^{-rn^{\theta}}\leq \left|q_n\right|\leq 2e^{-rn^{\theta}}, \theta\in (0,1), \end{equation*} which generalizes the results given by \cite{BJFA2005,CLSY,CMSW} to fractional nonlinear Schr\"{o}dinger equation.