University of Illinois at Urbana-Champaign, Department of Mathematics, Urbana, IL, 61801, USA
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.
(Online publication February 29 2012)
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