Solitons and Gibbs Measures for Nonlinear Schrodinger Equations

被引：2
|
作者：
Kirkpatrick, K. [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2012年 / 7卷 / 02期
基金：
美国国家科学基金会;
关键词：
NLS equation; statistical mechanics; invariant Gibbs measures; exact solvability; DATA CAUCHY-THEORY; CUBIC SCHRODINGER; INVARIANT-MEASURES; STATISTICAL-MECHANICS; ILL-POSEDNESS; DERIVATION; REGULARITY; EXISTENCE; DYNAMICS; ENERGY;
D O I：
10.1051/mmnp/20127209
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We review some recent results concerning Gibbs measures for nonlinear Schrodinger 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.
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页码：95 / 112
页数：18
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