Localization in periodic potentials : from Schrödinger operators to the Gross-Pitaevskii equation / / Dmitry E. Pelinovsky [[electronic resource]]
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| Autore: |
Pelinovsky Dmitry
|
| Titolo: |
Localization in periodic potentials : from Schrödinger operators to the Gross-Pitaevskii equation / / Dmitry E. Pelinovsky [[electronic resource]]
|
| Pubblicazione: | Cambridge : , : Cambridge University Press, , 2011 |
| Descrizione fisica: | 1 online resource (x, 398 pages) : digital, PDF file(s) |
| Disciplina: | 530.12/4 |
| Soggetto topico: | Schrödinger equation |
| Gross-Pitaevskii equations | |
| Localization theory | |
| Classificazione: | MAT000000 |
| MAT 356f | |
| Note generali: | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 1. Formalism of the nonlinear Schrödinger equations -- 2. Justification of the nonlinear Schrödinger equations -- 3. Existence of localized modes in periodic potentials -- 4. Stability of localized modes -- 5. Traveling localized modes in lattices -- Appendix A. Mathematical notations -- Appendix B. Selected topics of applied analysis. |
| Sommario/riassunto: | This book provides a comprehensive treatment of the Gross-Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose-Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross-Pitaevskii equation. It also serves as a reference for theoretical physicists interested in localization in periodic potentials. |
| Titolo autorizzato: | Localization in periodic potentials |
| ISBN: | 1-107-23231-7 |
| 9786613342591 | |
| 1-139-16162-8 | |
| 1-139-15781-7 | |
| 1-139-16062-1 | |
| 1-283-34259-6 | |
| 1-139-15605-5 | |
| 1-139-15957-7 | |
| 0-511-99775-2 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910781860403321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
London Mathematical Society lecture note series ; ; 390.