Localization in Periodic Potentials
eBook - PDF

Localization in Periodic Potentials

From Schrödinger Operators to the Gross–Pitaevskii Equation

  1. 410 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Localization in Periodic Potentials

From Schrödinger Operators to the Gross–Pitaevskii Equation

About this book

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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Information

Publisher
Cambridge University Press
Year
2011
Print ISBN
9781107621541
eBook ISBN
9781139154024
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Cover
  2. LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES
  3. Title
  4. Copyright
  5. To Anna and my children: Albert and Edward, Marta and Polina
  6. Contents
  7. Preface
  8. Formalism of the nonlinear Schrödinger equations
  9. Justification of the nonlinear Schrödinger equations
  10. Existence of localized modes in periodic potentials
  11. Stability of localized modes
  12. Traveling localized modes in lattices
  13. Appendix A
  14. Appendix B
  15. References
  16. Index

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Yes, you can access Localization in Periodic Potentials by Dmitry E. Pelinovsky in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.