000840228 000__ 03007cam\a2200409\a\4500 000840228 001__ 840228 000840228 005__ 20210515151536.0 000840228 006__ m\\\\\o\\d\\\\\\\\ 000840228 007__ cr\cn\nnnunnun 000840228 008__ 110615s2011\\\\enka\\\\ob\\\\001\0\eng\d 000840228 010__ $$z 2011025637 000840228 020__ $$z9781107621541 000840228 020__ $$z9781139157810$$q(electronic book) 000840228 035__ $$a(MiAaPQ)EBC807232 000840228 035__ $$a(Au-PeEL)EBL807232 000840228 035__ $$a(CaPaEBR)ebr10514101 000840228 035__ $$a(CaONFJC)MIL334259 000840228 035__ $$a(OCoLC)767579454 000840228 040__ $$aMiAaPQ$$cMiAaPQ$$dMiAaPQ 000840228 050_4 $$aQC174.26.W28$$bP45 2011 000840228 08204 $$a530.12/4$$223 000840228 1001_ $$aPelinovsky, Dmitry. 000840228 24510 $$aLocalization in periodic potentials$$h[electronic resource] :$$bfrom Schrödinger operators to the Gross-Pitaevskii equation /$$cDmitry E. Pelinovsky. 000840228 260__ $$aCambridge ;$$aNew York :$$bCambridge University Press,$$c2011. 000840228 300__ $$ax, 398 p. :$$bill. 000840228 4901_ $$aLondon Mathematical Society lecture note series ;$$v390 000840228 504__ $$aIncludes bibliographical references and index. 000840228 5058_ $$aMachine generated contents note: Preface; 1. Formalism of the nonlinear Schrödinger equations; 2. Justification of the nonlinear Schrödinger equations; 3. Existence of localized modes in periodic potentials; 4. Stability of localized modes; 5. Traveling localized modes in lattices; Appendix A. Mathematical notations; Appendix B. Selected topics of applied analysis; References; Index. 000840228 506__ $$aAccess limited to authorized users. 000840228 520__ $$a"This book provides a comprehensive treatment of the Gross-Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose-Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross-Pitaevskii equation. It also serves as a reference for theoretical physicists interested in localization in periodic potentials"--$$cProvided by publisher. 000840228 650_0 $$aSchrödinger equation. 000840228 650_0 $$aGross-Pitaevskii equations. 000840228 650_0 $$aLocalization theory. 000840228 830_0 $$aLondon Mathematical Society lecture note series ;$$v390. 000840228 852__ $$bebk 000840228 85640 $$3ProQuest Ebook Central Academic Complete$$uhttps://univsouthin.idm.oclc.org/login?url=https://ebookcentral.proquest.com/lib/usiricelib-ebooks/detail.action?docID=807232$$zOnline Access 000840228 909CO $$ooai:library.usi.edu:840228$$pGLOBAL_SET 000840228 980__ $$aEBOOK 000840228 980__ $$aBIB 000840228 982__ $$aEbook 000840228 983__ $$aOnline