Periodic and quasi-periodic solutions for the complex Ginzburg-Landau equation

被引：18

作者：

Chung, K. W. ^{[1
]}

Yuan, Xiaoping ^{[2
,3
]}

机构：

[1] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

来源：

NONLINEARITY | 2008年 / 21卷 / 03期

关键词：

D O I：

10.1088/0951-7715/21/3/004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that there are a continuous branch of periodic solutions and a Cantorian branch of quasi-periodic solutions for the complex Ginzburg-Landau equation for some coefficients of the linear driving term and the dissipation term and these solutions are normally hyperbolic.

引用

页码：435 / 451

页数：17

共 50 条

[1] INSTABILITY OF QUASI-PERIODIC SOLUTIONS OF THE GINZBURG-LANDAU EQUATION
DOELMAN, A
GARDNER, RA
JONES, CKRT
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1995, 125 : 501 - 517
[2] PERIODIC, QUASI-PERIODIC, AND CHAOTIC LOCALIZED SOLUTIONS OF THE QUINTIC COMPLEX GINZBURG-LANDAU EQUATION
DEISSLER, RJ
BRAND, HR
[J]. PHYSICAL REVIEW LETTERS, 1994, 72 (04) : 478 - 481
[3] Quasi-Periodic Solutions for the Generalized Ginzburg-Landau Equation with Derivatives in the Nonlinearity
Hongzi Cong
Meina Gao
[J]. Journal of Dynamics and Differential Equations, 2011, 23 : 1053 - 1074
[4] Quasi-Periodic Solutions for the Generalized Ginzburg-Landau Equation with Derivatives in the Nonlinearity
Cong, Hongzi
Gao, Meina
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2011, 23 (04) : 1053 - 1074
[5] Quasi-periodic solution for the complex Ginzburg-Landau equation with continuous spectrum
Li, Hepeng
Yuan, Xiaoping
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (11)
[6] Quasi-periodic solutions for the quasi-periodically forced cubic complex Ginzburg-Landau equation on Td
Cheng, Hongyu
Si, Jianguo
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (08)
[7] QUASI-PERIODIC SOLUTIONS FOR COMPLEX GINZBURG-LANDAU EQUATION OF NONLINEARITY |u|2pu
Cong, Hongzi
Liu, Jianjun
Yuan, Xiaoping
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (04): : 579 - 600
[8] INSTABILITY OF SPATIALLY QUASI-PERIODIC STATES OF THE GINZBURG-LANDAU EQUATION
BRIDGES, TJ
ROWLANDS, G
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1994, 444 (1921): : 347 - 362
[9] Exact periodic solutions of the complex Ginzburg-Landau equation
Porubov, AV
Velarde, MG
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1999, 40 (02) : 884 - 896
[10] Relative periodic solutions of the complex Ginzburg-Landau equation
López, V
Boyland, P
Heath, MT
Moser, RD
[J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2005, 4 (04): : 1042 - 1075

← 1 2 3 4 5 →