Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term

被引：0
|
作者：
Shu Qing Ma
Qian Shun Chang
机构：
[1] University of Alberta,Department of Mathematics Science
[2] Academy of Mathematics and System Sciences,Institute of Applied of Mathematics
[3] Chinese Academy of Sciences,undefined
来源：
Acta Mathematica Sinica | 2002年 / 18卷
关键词：
Attractor; NLS equation; 65N20; 39A10; 35B32;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we consider a semi-dicretized nonlinear Schrödinger (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.
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页码：779 / 800
页数：21
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