On scattering of small energy solutions of non-autonomous Hamiltonian nonlinear Schrödinger equations. (English) Zbl 1216.35134

The author revisits a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schrödinger equation (NLS) with an attractive localized potential and time-dependent factor in the nonlinearity. He shows 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.


35Q55 NLS equations (nonlinear Schrödinger equations)
35P25 Scattering theory for PDEs
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
35B44 Blow-up in context of PDEs
Full Text: DOI arXiv


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