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 language | English (US) |
|---|---|
| Pages (from-to) | 95-112 |
| Number of pages | 18 |
| Journal | Mathematical Modelling of Natural Phenomena |
| Volume | 7 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2012 |
Keywords
- Exact solvability
- Invariant Gibbs measures
- NLS equation
- Statistical mechanics
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics