In this paper, we consider a Hamiltonian system combining a nonlinear Schrödinger
equation (NLS) and an ordinary differential equation. This system is a simplified model
of the NLS around soliton solutions. Following Nakanishi , we show scattering of
L2 small H1 radial solutions. The proof is based on Nakanishi’s framework and Fermi
Golden Rule estimates on L4 in time norms.
