Solitons and gibbs measures for nonlinear schrödinger equations

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Abstract

We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.

Original languageEnglish (US)
Pages (from-to)95-112
Number of pages18
JournalMathematical Modelling of Natural Phenomena
Volume7
Issue number2
DOIs
StatePublished - 2012

Keywords

  • Exact solvability
  • Invariant Gibbs measures
  • NLS equation
  • Statistical mechanics

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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