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Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on $ h\mathbb{Z} $

  • * Corresponding author: Joackim Bernier

    * Corresponding author: Joackim Bernier
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  • We consider the discrete nonlinear Schrödinger equations on a one dimensional lattice of mesh $ h $, with a cubic focusing or defocusing nonlinearity. We prove a polynomial bound on the growth of the discrete Sobolev norms, uniformly with respect to the stepsize of the grid. This bound is based on a construction of higher modified energies.

    Mathematics Subject Classification: Primary: 35Q55, 37K60; Secondary: 65P99.

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