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KAM tori for quintic nonlinear schrödinger equations with given potential

  • * Corresponding author: Dongfeng Yan

    * Corresponding author: Dongfeng Yan

The first author is supported by NSFC grant 11371132, and the second author is supported by NSFC grant 11601487

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  • 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.

    Mathematics Subject Classification: Primary: 37K55; Secondary: 37J40.


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