Orbitally but not asymptotically stable ground states for the discrete NLS

Details Orbitally but not asymptotically stable ground states for the discrete NLS Orbitally but not asymptotically stable ground states for the discrete NLS

2008-11-17

arxiv.org/abs/0811.2701v1

Mathematics

Analysis of PDEs

Scientific paper

We consider examples of discrete nonlinear Schroedinger equations in Z admitting ground states which are orbitally but not asymptotically stable in l ^2(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 Schroedinger equations in eucliedean spaces. We do not investigate connections with work on quasi periodic solutions as in M.Johansson & S.Aubry and of Bambusi & Vella

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