We revisit a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schrödinger 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.
On scattering of small energy solutions of non-autonomous hamiltonian nonlinear Schrödinger equations / Cuccagna, Scipio. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 250:(2011), pp. 2347-2371. [10.1016/j.jde.2010.11.014]
On scattering of small energy solutions of non-autonomous hamiltonian nonlinear Schrödinger equations
CUCCAGNA, SCIPIO
2011-01-01
Abstract
We revisit a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schrödinger 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.Pubblicazioni consigliate
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