On nonlinear profile decompositions and scattering for a NLS-ODE model
Abstract
In this paper, we consider a Hamiltonian system combining a nonlinear Schr\" odinger equation (NLS) and an ordinary differential equation (ODE). This system is a simplified model of the NLS around soliton solutions. Following Nakanishi NakanishiJMSJ, 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.
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