Long time stability for the derivative nonlinear Schrödinger equation

被引：0
|
作者：
Liu, Jianjun [1 ]
Xiang, Duohui [1 ]
机构：
[1] Sichuan Univ, Sch Math, Chengdu 610065, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 537卷 / 02期
关键词：
Long time stability; Derivative nonlinear Schr & ouml; dinger; equation; Rational normal form; BIRKHOFF NORMAL-FORM; INVARIANT CANTOR MANIFOLDS; KLEIN-GORDON EQUATIONS; SCHRODINGER-EQUATION; PERIODIC SOLUTIONS; THEOREM; EXISTENCE;
D O I：
10.1016/j.jmaa.2024.128394
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the long time dynamics of the solutions of the derivative nonlinear Schr & ouml;dinger equation on one dimensional torus without external parameters. By using rational normal form, we prove the long time stability for generic small initial data. (c) 2024 Elsevier Inc. All rights reserved.
引用
收藏
页数：37
相关论文
共 50 条
  • [41] Orbital stability of periodic waves for the nonlinear Schrödinger equation
    Thierry Gallay
    Mariana Hǎrǎgus
    Journal of Dynamics and Differential Equations, 2007, 19 : 825 - 865
  • [42] Stability of Standing Waves for the Nonlinear Fractional Schrödinger Equation
    Jian Zhang
    Shihui Zhu
    Journal of Dynamics and Differential Equations, 2017, 29 : 1017 - 1030
  • [43] Stability of the traveling waves for the derivative Schrödinger equation in the energy space
    Changxing Miao
    Xingdong Tang
    Guixiang Xu
    Calculus of Variations and Partial Differential Equations, 2017, 56
  • [44] Orbital stability of a soliton solution for the derivative nonlinear Schrödinger equation in the L2 space
    Yang, Yiling
    Fan, Engui
    Liu, Yue
    MATHEMATISCHE ZEITSCHRIFT, 2025, 310 (02)
  • [45] The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation
    Xianguo Geng
    Huan Liu
    Journal of Nonlinear Science, 2018, 28 : 739 - 763
  • [46] Time Series Denoising Using Nonlinear Schrödinger Equation
    Lei Y.
    Song G.
    Gao C.
    Bao F.
    Zhang Y.
    Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics, 2021, 33 (08): : 1202 - 1209
  • [47] Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equation
    Rémi Carles
    Clotilde Fermanian-Kammerer
    Communications in Mathematical Physics, 2011, 301 : 443 - 472
  • [48] Long Time Stability of Some Small Amplitude Solutions in Nonlinear Schrödinger Equations
    Dario Bambusi
    Communications in Mathematical Physics, 1997, 189 : 205 - 226
  • [49] Derivation of Nonlinear Schrödinger Equation
    Xiang-Yao Wu
    Bai-Jun Zhang
    Xiao-Jing Liu
    Li Xiao
    Yi-Heng Wu
    Yan Wang
    Qing-Cai Wang
    Shuang Cheng
    International Journal of Theoretical Physics, 2010, 49 : 2437 - 2445
  • [50] On the quintic time-dependent coefficient derivative nonlinear Schrödinger equation in hydrodynamics or fiber optics
    Ting-Ting Jia
    Yi-Tian Gao
    Yu-Jie Feng
    Lei Hu
    Jing-Jing Su
    Liu-Qing Li
    Cui-Cui Ding
    Nonlinear Dynamics, 2019, 96 : 229 - 241
12345