Localization in periodic potentials : from Schrodinger operators to the Gross-Pitaevskii equation / / Dmitry E. Pelinovsky.
"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 e...
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Superior document: | London Mathematical Society lecture note series ; 390 |
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Year of Publication: | 2011 |
Language: | English |
Series: | London Mathematical Society lecture note series ;
390. |
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Physical Description: | x, 398 p. :; ill. |
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Pelinovsky, Dmitry. Localization in periodic potentials [electronic resource] : from Schrodinger operators to the Gross-Pitaevskii equation / Dmitry E. Pelinovsky. Cambridge ; New York : Cambridge University Press, 2011. x, 398 p. : ill. London Mathematical Society lecture note series ; 390 Includes bibliographical references and index. Machine generated contents note: Preface; 1. Formalism of the nonlinear Schrodinger equations; 2. Justification of the nonlinear Schrodinger 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; References; Index. "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 Schrodinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrodinger 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"-- Provided by publisher. Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. Schrodinger equation. Gross-Pitaevskii equations. Localization theory. Electronic books. ProQuest (Firm) London Mathematical Society lecture note series ; 390. https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=807232 Click to View |
language |
English |
format |
Electronic eBook |
author |
Pelinovsky, Dmitry. |
spellingShingle |
Pelinovsky, Dmitry. Localization in periodic potentials from Schrodinger operators to the Gross-Pitaevskii equation / London Mathematical Society lecture note series ; Machine generated contents note: Preface; 1. Formalism of the nonlinear Schrodinger equations; 2. Justification of the nonlinear Schrodinger 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; References; Index. |
author_facet |
Pelinovsky, Dmitry. ProQuest (Firm) ProQuest (Firm) |
author_variant |
d p dp |
author2 |
ProQuest (Firm) |
author2_role |
TeilnehmendeR |
author_corporate |
ProQuest (Firm) |
author_sort |
Pelinovsky, Dmitry. |
title |
Localization in periodic potentials from Schrodinger operators to the Gross-Pitaevskii equation / |
title_sub |
from Schrodinger operators to the Gross-Pitaevskii equation / |
title_full |
Localization in periodic potentials [electronic resource] : from Schrodinger operators to the Gross-Pitaevskii equation / Dmitry E. Pelinovsky. |
title_fullStr |
Localization in periodic potentials [electronic resource] : from Schrodinger operators to the Gross-Pitaevskii equation / Dmitry E. Pelinovsky. |
title_full_unstemmed |
Localization in periodic potentials [electronic resource] : from Schrodinger operators to the Gross-Pitaevskii equation / Dmitry E. Pelinovsky. |
title_auth |
Localization in periodic potentials from Schrodinger operators to the Gross-Pitaevskii equation / |
title_new |
Localization in periodic potentials |
title_sort |
localization in periodic potentials from schrodinger operators to the gross-pitaevskii equation / |
series |
London Mathematical Society lecture note series ; |
series2 |
London Mathematical Society lecture note series ; |
publisher |
Cambridge University Press, |
publishDate |
2011 |
physical |
x, 398 p. : ill. |
contents |
Machine generated contents note: Preface; 1. Formalism of the nonlinear Schrodinger equations; 2. Justification of the nonlinear Schrodinger 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; References; Index. |
isbn |
9781139157810 (electronic bk.) |
callnumber-first |
Q - Science |
callnumber-subject |
QC - Physics |
callnumber-label |
QC174 |
callnumber-sort |
QC 3174.26 W28 P45 42011 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=807232 |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
530 - Physics |
dewey-ones |
530 - Physics |
dewey-full |
530.12/4 |
dewey-sort |
3530.12 14 |
dewey-raw |
530.12/4 |
dewey-search |
530.12/4 |
oclc_num |
767579454 |
work_keys_str_mv |
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(MiAaPQ)500807232 (Au-PeEL)EBL807232 (CaPaEBR)ebr10514101 (CaONFJC)MIL334259 (OCoLC)767579454 |
hierarchy_parent_title |
London Mathematical Society lecture note series ; 390 |
hierarchy_sequence |
390. |
is_hierarchy_title |
Localization in periodic potentials from Schrodinger operators to the Gross-Pitaevskii equation / |
container_title |
London Mathematical Society lecture note series ; 390 |
author2_original_writing_str_mv |
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