| Issue |
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
|
|
|---|---|---|
| Page(s) | 95 - 112 | |
| DOI | https://doi.org/10.1051/mmnp/20127209 | |
| Published online | 29 February 2012 | |
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
University of Illinois at Urbana-Champaign, Department of
Mathematics, Urbana,
IL, 61801, USA
⋆ Corresponding author. E-mail: kkirkpat@illinois.edu
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.
Mathematics Subject Classification: 35Q55 / 81V70 / 81Q80
Key words: NLS equation / statistical mechanics / invariant Gibbs measures / exact solvability
© EDP Sciences, 2012
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