000 02753nam a22003738i 4500
001 CR9780511997754
003 UkCbUP
005 20200124160233.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 110112s2011||||enk o ||1 0|eng|d
020 _a9780511997754 (ebook)
020 _z9781107621541 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQC174.26.W28
_bP45 2011
082 0 0 _a530.12/4
_223
100 1 _aPelinovsky, Dmitry,
_eauthor.
245 1 0 _aLocalization in periodic potentials :
_bfrom Schrödinger operators to the Gross-Pitaevskii equation /
_cDmitry E. Pelinovsky.
264 1 _aCambridge :
_bCambridge University Press,
_c2011.
300 _a1 online resource (x, 398 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aLondon Mathematical Society lecture note series ;
_v390
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _a1. 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.
520 _aThis 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.
650 0 _aSchrödinger equation.
650 0 _aGross-Pitaevskii equations.
650 0 _aLocalization theory.
776 0 8 _iPrint version:
_z9781107621541
830 0 _aLondon Mathematical Society lecture note series ;
_v390.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511997754
999 _c517842
_d517840