Localization in periodic potentials [electronic resource] : from Schr�odinger operators to the Gross-Pitaevskii equation / Dmitry E. Pelinovsky.
By: Pelinovsky, Dmitry.
Contributor(s): ProQuest (Firm).
Material type:
BookSeries: London Mathematical Society lecture note series: 390.Publisher: Cambridge ; New York : Cambridge University Press, 2011Description: x, 398 p. : ill.Subject(s): Schr�odinger equation | Gross-Pitaevskii equations | Localization theoryGenre/Form: Electronic books.DDC classification: 530.12/4 Online resources: Click to View | Item type | Current location | Collection | Call number | URL | Copy number | Status | Date due | Item holds |
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E-book
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IUKL Library | Subscripti | https://ebookcentral.proquest.com/lib/kliuc-ebooks/detail.action?docID=807232 | 1 | Available |
Includes bibliographical references and index.
Machine generated contents note: Preface; 1. Formalism of the nonlinear Schr�odinger equations; 2. Justification of the nonlinear Schr�odinger 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 Schr�odinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schr�odinger 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.
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