Bifurcation from an equilibrium of the steady state Kuramoto-Sivashinsky equation in two spatial dimensions

被引：9

作者：

Li, CP ^{[1
]}

Chen, GR

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China

[2] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Hong Kong, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2002年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1142/S0218127402004176

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper deals with the steady state bifurcations of the Kuramoto-Sivashinsky (K-S) equation in two spatial dimensions with zero mean and periodic boundary value conditions. Applying the perturbation method, asymptotic expressions of the steady state solution branches that have bifurcated from the equilibrium are obtained. Furthermore, stability of the bifurcated solution branches is discussed.

引用

页码：103 / 114

页数：12

共 19 条

[1] Symmetry breaking Hopf bifurcations in equations with O(2) symmetry with application to the Kuramoto-Sivashinsky equation [J].

Amdjadi, F ;

Aston, PJ ;

Plechac, P .

JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 131 (01) :181-192

[2] LONG WAVES ON LIQUID FILMS [J].

BENNEY, DJ .

JOURNAL OF MATHEMATICS AND PHYSICS, 1966, 45 (02) :150-&

[3]

Changpin Li, 1998, APPL MATH JCU, V13, P263

[4]

Chow S-N., 2012, METHODS BIFURCATION

[5]

Foial C., 1988, J DIFF EQS, V73, P93

[6]

Golubitsky M., 1985, SINGULARITIES GROUPS

[7] PERSISTENT PROPAGATION OF CONCENTRATION WAVES IN DISSIPATIVE MEDIA FAR FROM THERMAL EQUILIBRIUM [J].

KURAMOTO, Y ;

TSUZUKI, T .

PROGRESS OF THEORETICAL PHYSICS, 1976, 55 (02) :356-369

[8] FORMATION OF DISSIPATIVE STRUCTURES IN REACTION-DIFFUSION SYSTEMS - REDUCTIVE PERTURBATION APPROACH [J].

KURAMOTO, Y ;

TSUZUKI, T .

PROGRESS OF THEORETICAL PHYSICS, 1975, 54 (03) :687-699

[9]

KURAMOTO Y, 1978, PROG THEOR PHYS S, V64, P346, DOI DOI 10.1143/PTPS.64.346

[10] Bifurcation analysis of the Kuramoto-Sivashinsky equation in one spatial dimension [J].

Li, CP ;

Chen, GR .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2001, 11 (09) :2493-2499

← 1 2 →