Double scattering channels for 1D NLS in the energy space and its generalization to higher dimensions |
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| Authors: | Luigi Forcella Nicola Visciglia |
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| Affiliation: | 1. Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy;2. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56100 Pisa, Italy |
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| Abstract: | We consider a class of 1D NLS perturbed with a steplike potential. We prove that the nonlinear solutions satisfy the double scattering channels in the energy space. The proof is based on concentration-compactness/rigidity method. We prove moreover that in dimension higher than one, classical scattering holds if the potential is periodic in all but one dimension and is steplike and repulsive in the remaining one. |
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| Keywords: | Corresponding author. |
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