On the existence of full dimensional KAM torus for nonlinear Schrödinger equation
On the existence of full dimensional KAM torus for nonlinear Schrödinger equation
In this paper, we study the following nonlinear Schrödinger equation \begin{document}$ \begin{eqnarray} \sqrt{-1}u_{t}-u_{xx}+V*u+\epsilon f(x)|u|^4u = 0, \ x\in\mathbb{T} = \mathbb{R}/2\pi\mathbb{Z}, ~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)\end{eqnarray} $\end{document} where $ V* $ is the Fourier multiplier defined by $ \widehat{(V* u})_n = V_{n}\widehat{u}_n, V_n\in[-1, 1] $ and $ f(x) $ is Gevrey smooth. It is shown …