Integrable discretization of nonlinear Schrodinger equation and its application with Fourier pseudo-spectral method

被引：3
|
作者：
Zhang, Y. [1 ]
Hu, X. B. [1 ]
Tam, H. W. [2 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China
[2] Hong Kong Baptist Univ, Dept Comp Sci, Hongkong, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2015年 / 69卷 / 04期
基金：
中国国家自然科学基金;
关键词：
NLS equation; Integrable discretization; Infinite conservation quantities; Fourier pseudo-spectral method; DISCRETE SOLITON-EQUATIONS; PARTIAL DIFFERENCE-EQUATIONS; DISPERSIVE DIELECTRIC FIBERS; NUMERICALLY INDUCED CHAOS; EVOLUTION-EQUATIONS; BACKLUND-TRANSFORMATIONS; OPTICAL PULSES; TIME; TRANSMISSION; SCHEMES;
D O I：
10.1007/s11075-014-9928-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new integrable discretization of the nonlinear SchrAodinger (NLS) equation is presented. Different from the one given by Ablowitz and Ladik, we discretize the time variable in this paper. The new discrete system converges to the NLS equation when we take a standard limit and has the same scattering operator as the original NLS equation. This indicates that both the new system and the NLS equation possess the same set of infinite conservation quantities. By applying the Fourier pseudo-spectral method to the space variable, we calculate the first five conservation quantities at different times. The numerical results indeed verify the conservation properties.
引用
收藏
页码：839 / 862
页数：24
相关论文
共 50 条
  • [1] Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method
    Y. Zhang
    X. B. Hu
    H. W. Tam
    Numerical Algorithms, 2015, 69 : 839 - 862
  • [2] A conservative Fourier pseudo-spectral method for the nonlinear Schrodinger equation
    Gong, Yuezheng
    Wang, Qi
    Wang, Yushun
    Cai, Jiaxiang
    JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 328 : 354 - 370
  • [3] An efficient and accurate Fourier pseudo-spectral method for the nonlinear Schrodinger equation with wave operator
    Li, Shan
    Wang, Tingchun
    Wang, Jialing
    Guo, Boling
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (02) : 340 - 356
  • [4] Optimal error estimate of a conformal Fourier pseudo-spectral method for the damped nonlinear Schrodinger equation
    Jiang, Chaolong
    Cai, Wenjun
    Wang, Yushun
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (04) : 1422 - 1454
  • [5] On the L∞ convergence of a conservative Fourier pseudo-spectral method for the space fractional nonlinear Schrodinger equation
    Xu, Zhuangzhi
    Cai, Wenjun
    Jiang, Chaolong
    Wang, Yushun
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 37 (02) : 1591 - 1611
  • [6] THE FOURIER PSEUDO-SPECTRAL METHOD FOR THE SRLW EQUATION
    郑家栋
    张汝芬
    郭本瑜
    Applied Mathematics and Mechanics(English Edition), 1989, (09) : 843 - 852
  • [7] Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrodinger equation
    Wang, Tingchun
    Wang, Jialing
    Guo, Boling
    JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 404 (404)
  • [8] A note on an integrable discretization of the nonlinear Schrodinger equation
    Black, W
    Weideman, JAC
    Herbst, BM
    INVERSE PROBLEMS, 1999, 15 (03) : 807 - 810
  • [9] A note on an integrable discretization of the nonlinear Schrodinger equation
    Suris, YB
    INVERSE PROBLEMS, 1997, 13 (04) : 1121 - 1136
  • [10] Numerical Solution of Nonlinear Schrodinger Equation by Using Time-Space Pseudo-Spectral Method
    Dehghan, Mehdi
    Taleei, Ameneh
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2010, 26 (04) : 979 - 992
12345