Orbitally but Not Asymptotically Stable Ground States for the Discrete Nls

  title={Orbitally but Not Asymptotically Stable Ground States for the Discrete Nls},
  author={Scipio Cuccagna},
We consider examples of discrete nonlinear Schrödinger equations in Z admitting ground states which are orbitally but not asymptotically stable in l(Z). The ground states contain internal modes which decouple from the continuous modes. The absence of leaking of energy from discrete to continues modes leads to an almost conservation and perpetual oscillation of the discrete modes. This is quite different from what is known for nonlinear Schrödinger equations in R. We do not investigate… CONTINUE READING

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