数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (3): 321-336.

• 论文 •    下一篇

STRANGE ATTRACTORS ON PSEUDOSPECTRAL
SOLUTIONS FOR DISSIPATIVE ZAKHAROV
EQUATIONS

马书清,常谦顺   

  1. Institute of Applied Mathematics, the Chinese Academy of Sciences, Beijing 100080, China
  • 出版日期:2004-07-20 发布日期:2004-07-20
  • 基金资助:

    This research is supported in part by National Natural Science
    Foundation of China and in part by State Key Laboratory of Scientific and Engineering Computing, Academia
    Sinica.

STRANGE ATTRACTORS ON PSEUDOSPECTRAL
SOLUTIONS FOR DISSIPATIVE ZAKHAROV
EQUATIONS

 MA Shu-Qing, CHANG Qian-Shun   

  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    This research is supported in part by National Natural Science
    Foundation of China and in part by State Key Laboratory of Scientific and Engineering Computing, Academia
    Sinica.

摘要:

In this paper, the pseudospectral method to solve the dissipative Zakharov
equations is used. Its convergence is proved by priori estimates. The existence of the global
attractors and the estimates of dimension are presented. A class of steady state solutions
is also disscussed. The numerical results show that if the steady state solutions satisfy
some special conditions, they become unstable and limit cycles and strange attractors will
occur for very small perturbations . The largest Lyapunov exponent and analysis of the
linearized system are applied to explain these phenomena.

Abstract:

In this paper, the pseudospectral method to solve the dissipative Zakharov
equations is used. Its convergence is proved by priori estimates. The existence of the global
attractors and the estimates of dimension are presented. A class of steady state solutions
is also disscussed. The numerical results show that if the steady state solutions satisfy
some special conditions, they become unstable and limit cycles and strange attractors will
occur for very small perturbations . The largest Lyapunov exponent and analysis of the
linearized system are applied to explain these phenomena.

Key words: Strange attractors, pseudospectral method;Zakharov equations

中图分类号: 

  • 65P20