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Solitons and Gibbs Measures for Nonlinear Schrödinger Equations

Published online by Cambridge University Press:  29 February 2012

K. Kirkpatrick
K. Kirkpatrick*
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, Urbana, IL, 61801, USA
*
⋆ Corresponding author. E-mail: kkirkpat@illinois.edu
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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.

Keywords

NLS equationstatistical mechanicsinvariant Gibbs measuresexact solvability
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 2: Solitary waves , 2012 , pp. 95 - 112
Copyright
© EDP Sciences, 2012

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