Stationary States for Nonlinear Schrödinger Equations with Periodic Potentials

Reika Fukuizumi, Andrea Sacchetti

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper we consider a one-dimensional non-linear Schrödinger equation with a periodic potential. In the semiclassical limit we prove the existence of stationary solutions by means of the reduction of the non-linear Schrödinger equation to a discrete non-linear Schrödinger equation. In particular, in the limit of large nonlinearity strength the stationary solutions turn out to be localized on a single lattice site of the periodic potential. A connection of these results with the Mott insulator phase for Bose-Einstein condensates in a one-dimensional periodic lattice is also discussed.

Original languageEnglish
Pages (from-to)707-738
Number of pages32
JournalJournal of Statistical Physics
Issue number4
Publication statusPublished - 2014 Jul


  • Bose-Einstein condensates in periodic lattices
  • Nonlinear Schrödinger and Discrete Nonlinear Schrödinger equations
  • Semiclassical approximation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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