EnglishIn this paper we consider a nonlinear Schr ̈odinger equation with a cubic nonlinearity and a multi-dimensional double well potential. In the semiclassical limit the problem of the existence of stationary solutions simply reduces to the analysis of a finite dimensional Hamiltonian system which exhibits different behaviour depending on the dimension. In particular, in dimension 1 the symmetric stationary solution shows a standard pitchfork bifurcation effect, while in dimensions 2 and 3 new asymmetrical solutions associated with saddle points occur. These last solutions are localized on a single well and this fact is related to the phase transition effect observed in Bose–Einstein condensates in periodical lattices.
| Data di pubblicazione: | 2014 |
| Titolo: | Stationary solutions to the multi-dimensional Gross–Pitaevskii equation with double-well potential |
| Autore/i: | A. Sacchetti |
| Autore/i UNIMORE: | |
| Digital Object Identifier (DOI): | 10.1088/0951-7715/27/11/2643 |
| Rivista: | |
| Volume: | 27 |
| Pagina iniziale: | 2643 |
| Pagina finale: | 2662 |
| Codice identificativo ISI: | WOS:000343931400002 |
| Codice identificativo Scopus: | 2-s2.0-84908066935 |
| Citazione: | Stationary solutions to the multi-dimensional Gross–Pitaevskii equation with double-well potential / A. Sacchetti. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 27(2014), pp. 2643-2662. |
| Tipologia | Articolo su rivista |
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| arxiv_52.pdf | Pre-print | Open Access Visualizza/Apri |
Utilizza questo identificativo per citare o creare un link a questo documento:
http://hdl.handle.net/11380/1046715
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