Solitons and Gibbs Measures for Nonlinear Schrödinger Equations

K. Kirkpatrick

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 2, page 95-112
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Kirkpatrick, K.. "Solitons and Gibbs Measures for Nonlinear Schrödinger Equations ." Mathematical Modelling of Natural Phenomena 7.2 (2012): 95-112. <http://eudml.org/doc/222230>.

@article{Kirkpatrick2012,
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.},
author = {Kirkpatrick, K.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {NLS equation; statistical mechanics; invariant Gibbs measures; exact solvability},
language = {eng},
month = {2},
number = {2},
pages = {95-112},
publisher = {EDP Sciences},
title = {Solitons and Gibbs Measures for Nonlinear Schrödinger Equations },
url = {http://eudml.org/doc/222230},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Kirkpatrick, K.
TI - Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/2//
PB - EDP Sciences
VL - 7
IS - 2
SP - 95
EP - 112
AB - 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.
LA - eng
KW - NLS equation; statistical mechanics; invariant Gibbs measures; exact solvability
UR - http://eudml.org/doc/222230
ER -

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