ON SMALL STATIONARY LOCALIZED SOLUTIONS FOR THE GENERALIZED 1-D SWIFT-HOHENBERG EQUATION

被引：34

作者：

GLEBSKY, LY ^{[1
]}

LERMAN, LM ^{[1
]}

机构：

[1] NIZHNII NOVOGOROD APPL MATH & CYBERNET RES INST,NIZHNII NOVGOROD 603600,RUSSIA

来源：

CHAOS | 1995年 / 5卷 / 02期

关键词：

D O I：

10.1063/1.166142

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of small localized stationary solutions for the generalized Swift-Hohenberg equation and find under some assumption a part of a boundary of their existence in the parameter plane. The related stationary equation creates a reversible Hamiltonian system with two degrees of freedom that undergoes the Hamiltonian-Hopf bifurcation with an additional degeneracy. We investigate this bifurcation in a two-parameter unfolding by means of the sixth-order normal form for the related Hamiltonian. The region where no localized solutions exist has been pointed out as well. © 1995 American Institute of Physics.

引用

页码：424 / 431

页数：8

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