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1 Burnside Mathematics- Operator Theory

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Other titles in the London Mathematical Society Lecture Notes series:

London Mathematical Society Lecture Note #390: Localization in Periodic Potentials: From Schr Dinger Operators to the Gross Pitaevskii Equation

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London Mathematical Society Lecture Note #390: Localization in Periodic Potentials: From Schr Dinger Operators to the Gross Pitaevskii Equation Cover

 

Synopses & Reviews

Publisher Comments:

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 dinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schr dinger 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.

Product Details

ISBN:
9781107621541
Author:
Pelinovsky, Dmitry E
Publisher:
Cambridge University Press
Author:
Pelinovsky, Dmitry E.
Subject:
Mathematics - General
Subject:
Mathematics-Applied
Copyright:
Publication Date:
20111031
Binding:
TRADE PAPER
Language:
English

Related Subjects

History and Social Science » Economics » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Operator Analysis
Science and Mathematics » Physics » Math

London Mathematical Society Lecture Note #390: Localization in Periodic Potentials: From Schr Dinger Operators to the Gross Pitaevskii Equation Used Trade Paper
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