数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 126-138.

• 论文 • 上一篇    下一篇

驻波广义Fisher-Kolmogorov方程的广义同宿轨

李晓培   

  1. 湛江师范学院数学与计算科学学院 广东 湛江 524048
  • 收稿日期:2012-07-14 修回日期:2013-06-25 出版日期:2014-02-25 发布日期:2014-02-25
  • 基金资助:

    广东省高等学校科技创新项目(2012KJCX0074)和湛江师范学院自然科学基金(LZL1101)资助.

Generalized Homoclinic Solutions for the Stationary Extended Fisher-Kolmogorov Equation

 LI Xiao-Pei   

  1. Department of Mathematics, Zhanjiang Normal University, Guangdong Zhanjiang 524048
  • Received:2012-07-14 Revised:2013-06-25 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    广东省高等学校科技创新项目(2012KJCX0074)和湛江师范学院自然科学基金(LZL1101)资助.

摘要:

研究驻波广义Fisher-Kolmogorov方程
u'''-βu''+ u3-u=0,   β>0.
该方程有一个鞍中心型平衡点u = 0 (一对非零实特征值和一对纯虚特征值). 应用扰动理论和调整相移, 证明对每一个正常数β该方程在原点附近有一个连接周期解的同宿轨(该文称为广义同宿轨).

关键词: 同宿轨, 周期解, 反转性

Abstract:

This paper investigates the stationary extended Fisher-Kolmogorov equation

u''''-βu''+ u3-u=0,  β>0,
which has a saddle-center equilibrium u = 0 (two nonzero real and two nonzero imaginary eigenvalues). Applying a perturbation method and adjusting some phase shift constants, we prove that it has a homoclinic solution connecting a periodic solution (called generalized homoclinic solution, thereafter) near the origin for each positive constant β.

Key words: Homoclinic solutions, Periodic solutions, Reversibility

中图分类号: 

  • 37C29