This paper is concerned with the 1-dimensional quintic nonlinear Schrödinger equations with real valued $ C^{\infty} $-smooth given potential
$ \sqrt{-1}u_{t} = u_{xx}-V(x)u-|u|^4u $
subject to Dirichlet boundary conditions. By means of normal form theory and an infinite-dimensional Kolmogorov-Arnold-Moser (KAM, for short) theorem, it is proved that the above equation admits a family of elliptic tori where lies small amplitude quasi-periodic solutions with two frequencies of high modes.
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