Localization in Periodic Potentials: From Schrödinger Operators to the Gross–Pitaevskii Equation

  • 407 pages
  • 1107621542
  • Anglais
  • Format Kindle
Localization in Periodic Potentials: From Schrödinger Operators to the Gross–Pitaevskii Equation

ᘸ Free Read Format Kindle [ Localization in Periodic Potentials: From Schrödinger Operators to the Gross–Pitaevskii Equation ] ᚝ Ebook By Dmitry E Pelinovsky 퐉 The book brilliantly harnesses powerful techniques, teaches them on the job and illustrates them with a profound and beautiful analysis of these equations, unreally real as suggested by one slogan of Chapter 2, a quote by Einstein, As far as the laws of mathematics refer to reality, they are not certain as far as they are certain, they do no refer to reality Emma Previato, Mathematics ReviewsThis 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. Introduction to Nonlinear Dispersive Equations Introduction Universitext Kindle edition by Felipe Linares, Gustavo Ponce Download it once and read on your device fuentenueva UGR Ph D students Mauricio Misquero mmisquero ugr, Vctor Ortega victortega ugr Preprints B Gebhard, R Ortega, Stability of periodic solutions Localization in Periodic Potentials: From Schrödinger Operators to the Gross–Pitaevskii Equation

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