Abstract
We revisit a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schr\" odinger equation (NLS) with an attractive localized potential and a time-dependent factor in the nonlinearity. We show that, under generic hypotheses on the linearization at 0 of the equation, small energy solutions are asymptotically free. This is yet a new application of the hamiltonian structure, continuing a program initiated in a paper by Bambusi and Cuccagna.
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