Geodesic
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
K. Kirkpatrick1
1 University of Illinois at Urbana-Champaign, Department of Mathematics, Urbana, IL, 61801, USA
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 95-112.

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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.
DOI : 10.1051/mmnp/20127209

K. Kirkpatrick 1

1 University of Illinois at Urbana-Champaign, Department of Mathematics, Urbana, IL, 61801, USA 
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K. Kirkpatrick. Solitons and Gibbs Measures for Nonlinear Schrödinger Equations. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 95-112. doi : 10.1051/mmnp/20127209. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127209/

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