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arXiv · 1701.02849

On nonlinear profile decompositions and scattering for a NLS-ODE model

Scipio Cuccagna·Masaya Maeda
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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 \cite{NakanishiJMSJ}, we show scattering of $L^2$ small $H^1$ radial solutions. The proof is based on Nakanishi's framework and Fermi Golden Rule estimates on $L^4$ in time norms.

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Scipio Cuccagna, Masaya Maeda. 2017-01-11. On nonlinear profile decompositions and scattering for a NLS-ODE model. https://arxiv.org/abs/1701.02849

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