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.
引用
收藏
页码：95 / 112
页数：18
相关论文
共 50 条
  • [41] Collisions of two solitons in an arbitrary number of coupled nonlinear Schrodinger equations
    Soljacic, M
    Steiglitz, K
    Sears, SM
    Segev, M
    Jakubowski, MH
    Squier, R
    PHYSICAL REVIEW LETTERS, 2003, 90 (25)
  • [42] Vector periodic solitons for three-coupled nonlinear Schrodinger equations
    Wang, Xiao-Min
    Zhang, Ling-Ling
    Wang, Xiao-Qiang
    MODERN PHYSICS LETTERS B, 2018, 32 (26):
  • [43] On distinctive solitons type solutions for some important nonlinear Schrodinger equations
    Osman, M. S.
    Machado, J. A. T.
    Baleanu, D.
    Zafar, A.
    Raheel, M.
    OPTICAL AND QUANTUM ELECTRONICS, 2021, 53 (02)
  • [44] Construction of multi-solitons and multi kink-solitons of derivative nonlinear Schrodinger equations
    Phan Van Tin
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 221
  • [45] Numerical Invariant Measures for Damped Stochastic Nonlinear Schrodinger Equations
    Hong, Jialin
    Wang, Xu
    INVARIANT MEASURES FOR STOCHASTIC NONLINEAR SCHRODINGER EQUATIONS: NUMERICAL APPROXIMATIONS AND SYMPLECTIC STRUCTURES, 2019, 2251 : 109 - 152
  • [46] Conservation laws and solitons for the coupled cubic-quintic nonlinear Schrodinger equations in nonlinear optics
    Shan, Wen-Rui
    Qi, Feng-Hua
    Guo, Rui
    Xue, Yu-Shan
    Wang, Pan
    Tian, Bo
    PHYSICA SCRIPTA, 2012, 85 (01)
  • [47] ANGULAR VECTOR SOLITONS OF THE COUPLED NONLINEAR SCHRODINGER EQUATIONS WITH SPATIALLY MODULATED NONLINEARITIES
    Cao, Ruo-Yun
    Zhong, Wei-Ping
    Mihalache, Dumitru
    ROMANIAN REPORTS IN PHYSICS, 2015, 67 (02) : 375 - 385
  • [48] High-speed excited multi-solitons in nonlinear Schrodinger equations
    Cote, Raphael
    Le Coz, Stefan
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2011, 96 (02): : 135 - 166
  • [49] Dark solitons in N-coupled higher order nonlinear Schrodinger equations
    Seenuvasakumaran, P.
    Mahalingam, A.
    Porsezian, K.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (07) : 1318 - 1328
  • [50] Stability of Algebraic Solitons for Nonlinear Schrodinger Equations of Derivative Type: Variational Approach
    Hayashi, Masayuki
    ANNALES HENRI POINCARE, 2022, 23 (12): : 4249 - 4277
12345