The nonlinear Schrödinger equation with a random potential: Results and puzzles

Shmuel Fishman, Yevgeny Krivolapov, Avy Soffer

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

The nonlinear Schrödinger equation (NLSE) with a random potential is motivated by experiments in optics and in atom optics and is a paradigm for the competition between the randomness and nonlinearity. The analysis of the NLSE with a random (Anderson like) potential has been done at various levels of control: numerical, analytical and rigorous. Yet this model equation presents us with a highly inconclusive and often contradictory picture. We will describe the main recent results obtained in this field and propose a list of specific problems to focus on, which we hope will enable to resolve these outstanding questions.

Original languageEnglish (US)
Pages (from-to)R53-R72
JournalNonlinearity
Volume25
Issue number4
DOIs
StatePublished - Apr 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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