Semiclassical asymptotics for weakly nonlinear Bloch waves

Rémi Carles, Peter A. Markowich, Christof Sparber

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

Original languageEnglish (US)
Pages (from-to)343-375
Number of pages33
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 2004
Externally publishedYes


  • Bloch eigenvalue problem
  • Bose-Einstein condensate
  • Nonlinear Schrödinger equation
  • WKB-asymptotics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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