On scattering of small energy solutions of non autonomous hamiltonian nonlinear Schrödinger equations

Details On scattering of small energy solutions of non autonomous hamiltonian nonlinear Schrödinger equations On scattering of small energy solutions of non autonomous hamiltonian nonlinear Schrödinger equations

2010-06-15

arxiv.org/abs/1006.2968v1

Mathematics

Analysis of PDEs

Scientific paper

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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