Localization in Periodic Potentials
Localization in Periodic Potentials
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$102.00
USDThis 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.
- Assembles individual results scattered across the literature
- Suitable text for graduate students in applied mathematics studying nonlinear waves
- Provides a solid mathematical foundation for students and young researchers specializing in the theory of Bose–Einstein condensation
Reviews & endorsements
"The book brilliantly harnesses powerful techniques, teaches them "on-the-job" and illustrates them with a profound and beautiful analysis of these equations, unreally real as suggested by one slogan of Chapter 2, a quote by Einstein, :As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do no refer to reality."
Emma Previato, Mathematics Reviews
Product details
November 2011Adobe eBook Reader
9781139154024
0 pages
0kg
35 b/w illus. 165 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- 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
- References
- Index.
