Localized periodic patterns for the non-symmetric generalized Swift-Hohenberg equation

被引：32

作者：

Budd, CJ

Kuske, R

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Univ Bath, Ctr Nonlinear Mech, Bath BA2 7AY, Avon, England

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2005年 / 208卷 / 1-2期

基金：

加拿大自然科学与工程研究理事会;

关键词：

asymptotic balance; localized patterns; Lagrangian; heteroclinic connection;

D O I：

10.1016/j.physd.2005.06.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new asymptotic multiple scale expansion is used to derive envelope equations for localized spatially periodic patterns in the context of the generalized Swift-Hohenberg equation. An analysis of this envelope equation results in parametric conditions for localized patterns. Furthermore, it yields corrections for wave number selection which are an order of magnitude larger for asymmetric nonlinearities than for the symmetric case. The analytical results are compared with numerical computations which demonstrate that the condition for localized patterns coincides with vanishing Hamiltonian and Lagrangian for periodic solutions. One striking feature of the choice of scaling parameters is that the derived condition for localized patterns agrees with the numerical results for a significant range of parameters which are an 0(l) distance from the bifurcation, thus providing a novel approach for studying these localized patterns. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：73 / 95

页数：23

共 24 条

[1]

Ackemann T., 2003, 2003 European Quantum Electronics Conference. EQEC 2003 (IEEE Cat No.03TH8665), DOI 10.1109/EQEC.2003.1313957

[2]

[Anonymous], 1990, DISSIPATIVE STRUCTUR, DOI DOI 10.1016/B978-0-08-092445-8.50011-0

[3]

Bar M, 1995, PHYS REV E, V52, pR5739

[4] Bifurcations of periodic solutions satisfying the zero-Hamiltonian constraint in reversible differential equations [J].

Beardmore, RE ;

Peletier, MA ;

Budd, CJ ;

Wadee, MA .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 36 (05) :1461-1488

[5] Abundance of stable stationary localized solutions to the generalized 1D Swift-Hohenberg equation [J].

Belyakov, LA ;

Glebsky, LY ;

Lerman, LM .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 34 (2-4) :253-266

[6] NONADIABATIC EFFECTS IN CONVECTION [J].

BENSIMON, D ;

SHRAIMAN, BI ;

CROQUETTE, V .

PHYSICAL REVIEW A, 1988, 38 (10) :5461-5464

[7] Asymptotics of cellular buckling close to the Maxwell load [J].

Budd, CJ ;

Hunt, GW ;

Kuske, R .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2016) :2935-2964

[8] A global characterization of gap solitary-wave solutions to a coupled KdV system [J].

Champneys, A ;

Groves, MD ;

Woods, PD .

PHYSICS LETTERS A, 2000, 271 (03) :178-190

[9] Stable static localized structures in one dimension [J].

Coullet, P ;

Riera, C ;

Tresser, C .

PHYSICAL REVIEW LETTERS, 2000, 84 (14) :3069-3072

[10] Oscillon-type structures and their interaction in a Swift-Hohenberg model [J].

Crawford, C ;

Riecke, H .

PHYSICA D-NONLINEAR PHENOMENA, 1999, 129 (1-2) :83-92

← 1 2 3 →