Orbitally but not asymptotically stable ground states for the discrete NLS

Abstract

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

References in corpus (4)

• Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations
• On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension
• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$
• On instability of excited states of the nonlinear Schrödinger equation