Attractors and dimensions for discretizations of a NLS equation with a non-local nonlinear term

被引：0

作者：

Ma, SQ ^{[1
]}

Chang, QS

机构：

[1] Univ Alberta, Dept Math Sci, Edmonton, AB T6G 2G1, Canada

[2] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2002年 / 18卷 / 04期

基金：

中国国家自然科学基金;

关键词：

attractor; NLS equation;

D O I：

10.1007/s10114-002-0207-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a semi-dicretized nonlinear Schrodinger (NLS) equation with local integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained, and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments are given and many interesting phenomena are observed such as limit cycles, chaotic attractors and a so-called crisis of the chaotic attractors.

引用

页码：779 / 800

页数：22

共 50 条

[1] Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term
Shu Qing MA
Qian Shun CHANG Department of Mathematics Science. University of Alberta. Canada T6G 2G1 Institute of Applied Mathematics. Academy of Mathematics and System Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. China
[J]. Acta Mathematica Sinica,English Series, 2002, 18 (04) : 779 - 800
[2] Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term
Shu Qing Ma
Qian Shun Chang
[J]. Acta Mathematica Sinica, 2002, 18 : 779 - 800
[3] Reduced Non-Local Integrable NLS Hierarchies by Pairs of Local and Non-Local Constraints
Wen-Xiu Ma
[J]. International Journal of Applied and Computational Mathematics, 2022, 8 (4)
[4] On the wave equation with a temporal non-local term
Medjden, Mohamed
Tatar, Nasser-Eddinne
[J]. DYNAMIC SYSTEMS AND APPLICATIONS, 2007, 16 (04): : 665 - 671
[5] Nonlinear degenerate parabolic equation with non-local source
Weibing D.
Chunhong X.
[J]. Applied Mathematics-A Journal of Chinese Universities, 2002, 17 (2) : 171 - 176
[6] A NONLINEAR DEGENERATE PARABOLIC EQUATION WITH NON-LOCAL SOURCE
Deng Weibing Xie ChunhongDept.ofMath.
[J]. Applied Mathematics:A Journal of Chinese Universities, 2002, (02) : 171 - 176
[7] Scattering theory for the Dirac equation with a non-local term
Machihara, Shuji
Tsutaya, Kimitoshi
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2009, 139 : 867 - 878
[8] ATTRACTORS AND DIMENSIONS FOR DISCRETIZATIONS OF A WEAKLY DAMPED SCHRODINGER-EQUATION AND A SINE-GORDEN EQUATION
YAN, Y
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (12) : 1417 - 1452
[9] Nonlinear non-local elliptic equation modelling electrostatic actuation
Lin, Fanghua
Yang, Yisong
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2007, 463 (2081): : 1323 - 1337
[10] Non-local problems in time for one nonlinear parabolic equation
Shapatava, A
[J]. METMBS '05: PROCEEDINGS OF THE 2005 INTERNATIONAL CONFERENCE ON MATHEMATICS AND ENGINEERING TECHNIQUES IN MEDICINE AND BIOLOGICAL SCIENCES, 2005, : 197 - 200

← 1 2 3 4 5 →