Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrodinger equation

被引：15
|
作者：
Genovese, Giuseppe [1 ]
Luca, Renato [2 ]
Valeri, Daniele [3 ]
机构：
[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland
[2] CSIC, Inst Ciencias Matemat, E-28049 Madrid, Spain
[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China
来源：
SELECTA MATHEMATICA-NEW SERIES | 2016年 / 22卷 / 03期
基金：
瑞士国家科学基金会; 欧洲研究理事会;
关键词：
Gibbs measures; DNLS; Integrable systems; GLOBAL WELL-POSEDNESS; INVARIANT-MEASURES; STATISTICAL-MECHANICS;
D O I：
10.1007/s00029-016-0225-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the one-dimensional periodic derivative nonlinear Schrodinger equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion , . In each the term with the highest regularity involves the Sobolev norm of the solution of the DNLS equation. We show that a functional measure on , absolutely continuous w.r.t. the Gaussian measure with covariance , is associated to each integral of motion, k >= 1 .
引用
收藏
页码：1663 / 1702
页数：40
相关论文
共 50 条
  • [1] Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
    Giuseppe Genovese
    Renato Lucà
    Daniele Valeri
    Selecta Mathematica, 2016, 22 : 1663 - 1702
  • [2] Gibbs measure for the periodic derivative nonlinear Schrodinger equation
    Thomann, Laurent
    Tzvetkov, Nikolay
    NONLINEARITY, 2010, 23 (11) : 2771 - 2791
  • [3] Invariant measures for the periodic derivative nonlinear Schrodinger equation
    Genovese, Giuseppe
    Luca, Renato
    Valeri, Daniele
    MATHEMATISCHE ANNALEN, 2019, 374 (3-4) : 1075 - 1138
  • [4] Periodic solutions of a derivative nonlinear Schrodinger equation: Elliptic integrals of the third kind
    Chow, K. W.
    Ng, T. W.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (13) : 3825 - 3830
  • [5] Periodic and quasi-periodic solutions of a derivative nonlinear Schrodinger equation
    Liu, Jie
    APPLICABLE ANALYSIS, 2016, 95 (04) : 801 - 825
  • [6] Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrodinger equation
    Isom, Bradley
    Mantzavinos, Dionyssios
    Stefanov, Atanas
    MATHEMATISCHE ANNALEN, 2024, 388 (03) : 2289 - 2329
  • [7] Periodic Wave Solutions of Generalized Derivative Nonlinear Schrodinger Equation
    Zha Qi-Lao
    Li Zhi-Bin
    CHINESE PHYSICS LETTERS, 2008, 25 (11) : 3844 - 3847
  • [8] Localized Waves on the Periodic Background for the Derivative Nonlinear Schrodinger Equation
    Wu, Lifei
    Zhang, Yi
    Ye, Rusuo
    Jin, Jie
    NONLINEAR AND MODERN MATHEMATICAL PHYSICS, NMMP 2022, 2024, 459 : 335 - 347
  • [9] ON THE LIFESPAN OF STRONG SOLUTIONS TO THE PERIODIC DERIVATIVE NONLINEAR SCHRODINGER EQUATION
    Fujiwara, Kazumasa
    Ozawa, Tohru
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2018, 7 (02): : 275 - 280
  • [10] Periodic dynamics of a derivative nonlinear Schrodinger equation with variable coefficients
    Liu, Qihuai
    Liu, Wenye
    Torres, Pedro J.
    Huang, Wentao
    APPLICABLE ANALYSIS, 2020, 99 (03) : 407 - 427
12345