Orbitally but not asymptotically stable ground states for the discrete NLS

2008/11/17 by Scipio Cuccagna, Cuccagna, Scipio
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0811.2701

openalex publication_date 2008/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• On asymptotic stability of standing waves of discrete Schrödinger equation in \Bbb Z
• On instability of excited states of the nonlinear Schrödinger equation

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