On small energy stabilization in the NLS with a trapping potential

Abstract

We describe the asymptotic behavior of small energy solutions of an NLS with a trapping potential. In particular we generalize work of Soffer and Weinstein, and of Tsai et. al. The novelty is that we allow generic spectra associated to the potential. This is yet a new application of the idea to interpret the nonlinear Fermi Golden Rule as a consequence of the Hamiltonian structure.

Revised version

References in corpus (5)

• Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations
• Selection of the ground state for nonlinear Schroedinger equations
• Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
• Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit
• Hamiltonian Hopf bifurcations and chaos of NLS/GP standing-wave modes

Cited by in corpus (2)

• On orbital instability of spectrally stable vortices of the NLS in the plane
• On ground states for the 2D Schrodinger equation with combined nonlinearities and harmonic potential