TY - BOOK ID - 80826192 TI - Localization in periodic potentials PY - 2011 SN - 9780511997754 9781107621541 0511997752 9781139161626 1139161628 9781139157810 1139157817 9781139157810 1107621542 9781139159579 1139159577 9786613342591 6613342599 1107232317 1139160621 1283342596 1139156055 9781107232310 9781139160629 9781283342599 9781139156059 PB - Cambridge Cambridge University Press DB - UniCat KW - Schrödinger equation. KW - Gross-Pitaevskii equations. KW - Localization theory. KW - Categories (Mathematics) KW - Homotopy theory KW - Nilpotent groups KW - Equations, Gross-Pitaevskii KW - Nonlinear Schrödinger equations KW - Schrödinger equations, Nonlinear KW - Differential equations, Nonlinear KW - Nonlinear wave equations KW - Equation, Schrödinger KW - Schrödinger wave equation KW - Differential equations, Partial KW - Particles (Nuclear physics) KW - Wave mechanics KW - WKB approximation UR - https://www.unicat.be/uniCat?func=search&query=sysid:80826192 AB - 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. ER -