中国物理B ›› 2015, Vol. 24 ›› Issue (12): 120401-120401.doi: 10.1088/1674-1056/24/12/120401

• GENERAL • 上一篇    下一篇

Unstable and exact periodic solutions of three-particles time-dependent FPU chains

刘期怀a b, 邢明燕a, 李新祥c, 王超d   

  1. a School of Mathematics and Computing Sciences, Guilin University of Electronic Technology, Guilin 541002, China;
    b Guangxi Experiment Center of Information Science, Guilin 541001, China;
    c College of Sciences, Shanghai University, Shanghai 200444, China;
    d School of Mathematic Sciences, Yancheng Teacher's University, Yancheng 224002, China
  • 收稿日期:2015-04-20 修回日期:2015-08-18 出版日期:2015-12-05 发布日期:2015-12-05
  • 通讯作者: Xing Ming-Yan E-mail:xinxiang.lee@t.shu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11301106, 11201288, and 11261013), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2014GXNSFBA118017), the Innovation Project of Graduate Education of Guangxi Zhuang Autonomous Region, China, (Grant No. YCSZ2014143), and the Guangxi Experiment Center of Information Science (Grant No. YB1410).

Unstable and exact periodic solutions of three-particles time-dependent FPU chains

Liu Qi-Huai (刘期怀)a b, Xing Ming-Yan (邢明燕)a, Li Xin-Xiang (李新祥)c, Wang Chao (王超)d   

  1. a School of Mathematics and Computing Sciences, Guilin University of Electronic Technology, Guilin 541002, China;
    b Guangxi Experiment Center of Information Science, Guilin 541001, China;
    c College of Sciences, Shanghai University, Shanghai 200444, China;
    d School of Mathematic Sciences, Yancheng Teacher's University, Yancheng 224002, China
  • Received:2015-04-20 Revised:2015-08-18 Online:2015-12-05 Published:2015-12-05
  • Contact: Xing Ming-Yan E-mail:xinxiang.lee@t.shu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11301106, 11201288, and 11261013), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2014GXNSFBA118017), the Innovation Project of Graduate Education of Guangxi Zhuang Autonomous Region, China, (Grant No. YCSZ2014143), and the Guangxi Experiment Center of Information Science (Grant No. YB1410).

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摘要： For lower dimensional Fermi-Pasta-Ulam (FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the Hénon-Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional α β-FPU model composed of three particles with periodic boundary conditions.

关键词: periodic solution, stability, method of averaging

Abstract: For lower dimensional Fermi-Pasta-Ulam (FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the Hénon-Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional α β-FPU model composed of three particles with periodic boundary conditions.

Key words: periodic solution, stability, method of averaging

中图分类号:  (Exact solutions)

  • 04.20.Jb
02.60.-x (Numerical approximation and analysis) 02.30.Hq (Ordinary differential equations)