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exact solvability

Mathematical Modelling of Natural Phenomena (1)

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Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
K. Kirkpatrick
Journal:

Mathematical Modelling of Natural Phenomena / Volume 7 / Issue 2 / 2012

Published online by Cambridge University Press:

29 February 2012, pp. 95-112

Print publication:

2012
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We review some recent results concerning Gibbs measures for nonlinear Schrödingerequations (NLS), with implications for the theory of the NLS, including stability andtypicality of solitary wave structures. In particular, we discuss the Gibbs measures ofthe discrete NLS in three dimensions, where there is a striking phase transition tosoliton-like behavior.