The Existence of Exponential Attractor for Discrete Ginzburg-Landau Equation-Reference-Cited by-同舟云学术

The Existence of Exponential Attractor for Discrete Ginzburg-Landau Equation

Published:2015 Issue: Volume:2015 Page:1-6
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Du Guangyin¹,Zhu Zeqi²,Zhao Caidi³

Affiliation:

1. Institute of Geotechnical Engineering, Southeast University, Nanjing, Jiangsu 210096, China

2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China

3. Department of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Abstract

This paper studies the following discrete systems of the complex Ginzburg-Landau equation:iu˙m-(α-iε)(2um-um+1-um-1)+iκum+βum2σum=gm, m∈Z. Under some conditions on the parametersα, ε, κ, β, andσ, we prove the existence of exponential attractor for the semigroup associated with these discrete systems.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modeling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2015/217608.pdf

Reference39 articles.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Exponentially stable breather solutions in nonautonomous dissipative nonlinear Schrödinger lattices;Applicable Analysis;2024-05-17

2. Dynamics of nonlocal and local discrete Ginzburg–Landau equations: Global attractors and their congruence;Nonlinear Analysis;2022-02

3. Existence and Congruence of Global Attractors for Damped and Forced Integrable and Nonintegrable Discrete Nonlinear Schrödinger Equations;Journal of Dynamics and Differential Equations;2021-11-24