1.

Record Nr.

UNINA9910457512503321

Autore

Pelinovsky Dmitry

Titolo

Localization in periodic potentials : from Schrödinger operators to the Gross-Pitaevskii equation / / Dmitry E. Pelinovsky [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2011

ISBN

1-107-23231-7

9786613342591

1-139-16162-8

1-139-15781-7

1-139-16062-1

1-283-34259-6

1-139-15605-5

1-139-15957-7

0-511-99775-2

Descrizione fisica

1 online resource (x, 398 pages) : digital, PDF file(s)

Collana

London Mathematical Society lecture note series ; ; 390

Disciplina

530.12/4

Soggetti

Schrödinger equation

Gross-Pitaevskii equations

Localization theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.