Localization in periodic potentials: from Schrödinger operators to the Gross-Pitaevskii equation
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 existen...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2011
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| Series: | London Mathematical Society lecture note series
390 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (x, 398 pages) |
| ISBN: | 9780511997754 |
| DOI: | 10.1017/CBO9780511997754 |
Staff View
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| 505 | 8 | |a 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 | |
| 520 | |a 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 | ||
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Record in the Search Index
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| any_adam_object | |
| author | Pelinovsky, Dmitry |
| author_facet | Pelinovsky, Dmitry |
| author_role | aut |
| author_sort | Pelinovsky, Dmitry |
| author_variant | d p dp |
| building | Verbundindex |
| bvnumber | BV043941697 |
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| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511997754 (OCoLC)852518135 (DE-599)BVBBV043941697 |
| dewey-full | 530.12/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/4 |
| dewey-search | 530.12/4 |
| dewey-sort | 3530.12 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511997754 |
| format | Electronic eBook |
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| id | DE-604.BV043941697 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511997754 |
| language | English |
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| spelling | Pelinovsky, Dmitry Verfasser aut Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation Dmitry E. Pelinovsky Cambridge Cambridge University Press 2011 1 online resource (x, 398 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 390 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Schrödinger equation Gross-Pitaevskii equations Localization theory Periodisches Potenzial (DE-588)4232802-0 gnd rswk-swf Lokalisationstheorie (DE-588)4203492-9 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s Periodisches Potenzial (DE-588)4232802-0 s Lokalisationstheorie (DE-588)4203492-9 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-107-62154-1 https://doi.org/10.1017/CBO9780511997754 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pelinovsky, Dmitry Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation 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 Schrödinger equation Gross-Pitaevskii equations Localization theory Periodisches Potenzial (DE-588)4232802-0 gnd Lokalisationstheorie (DE-588)4203492-9 gnd Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd |
| subject_GND | (DE-588)4232802-0 (DE-588)4203492-9 (DE-588)4278277-6 |
| title | Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation |
| title_auth | Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation |
| title_exact_search | Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation |
| title_full | Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation Dmitry E. Pelinovsky |
| title_fullStr | Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation Dmitry E. Pelinovsky |
| title_full_unstemmed | Localization in periodic potentials from Schrödinger operators to the Gross-Pitaevskii equation Dmitry E. Pelinovsky |
| title_short | Localization in periodic potentials |
| title_sort | localization in periodic potentials from schrodinger operators to the gross pitaevskii equation |
| title_sub | from Schrödinger operators to the Gross-Pitaevskii equation |
| topic | Schrödinger equation Gross-Pitaevskii equations Localization theory Periodisches Potenzial (DE-588)4232802-0 gnd Lokalisationstheorie (DE-588)4203492-9 gnd Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd |
| topic_facet | Schrödinger equation Gross-Pitaevskii equations Localization theory Periodisches Potenzial Lokalisationstheorie Nichtlineare Schrödinger-Gleichung |
| url | https://doi.org/10.1017/CBO9780511997754 |
| work_keys_str_mv | AT pelinovskydmitry localizationinperiodicpotentialsfromschrodingeroperatorstothegrosspitaevskiiequation |