EnglishWe study the nature of the nonlinear Schrödinger equation ground states on the product spaces Rn x Mk , where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding Rn ground states. We also prove that above a critical mass the ground states have nontrivial Mk dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.
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http://hdl.handle.net/11568/214351| Autori interni: | VISCIGLIA, NICOLA |
| Autori: | S. Terracini; N. Tzvetkov; N. Visciglia |
| Titolo: | The nonlinear Schrödinger equation ground states on product spaces |
| Anno del prodotto: | 2014 |
| Abstract: | We study the nature of the nonlinear Schrödinger equation ground states on the product spaces Rn x Mk , where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding Rn ground states. We also prove that above a critical mass the ground states have nontrivial Mk dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results. |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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|---|---|---|---|---|
| Visciglia_214351.pdf | Editoriale |  | Open Access Visualizza/Apri |
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