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Chin. Phys. B, 2015, Vol. 24(12): 120401    DOI: 10.1088/1674-1056/24/12/120401
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Unstable and exact periodic solutions of three-particles time-dependent FPU chains

Liu Qi-Huaia b, Xing Ming-Yana, Li Xin-Xiangc, Wang Chaod
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
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.
Keywords:  periodic solution      stability      method of averaging  
Received:  20 April 2015      Revised:  18 August 2015      Published:  05 December 2015
PACS:  04.20.Jb (Exact solutions)  
  02.60.-x (Numerical approximation and analysis)  
  02.30.Hq (Ordinary differential equations)  
Fund: 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).
Corresponding Authors:  Xing Ming-Yan     E-mail:

Cite this article: 

Liu Qi-Huai, Xing Ming-Yan, Li Xin-Xiang, Wang Chao Unstable and exact periodic solutions of three-particles time-dependent FPU chains 2015 Chin. Phys. B 24 120401

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