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

doi:10.1088/1674-1056/24/12/120401

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
Accepted manuscript online:

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: xinxiang.lee@t.shu.edu.cn

Cite this article:

Liu Qi-Huai (刘期怀), Xing Ming-Yan (邢明燕), Li Xin-Xiang (李新祥), Wang Chao (王超) Unstable and exact periodic solutions of three-particles time-dependent FPU chains 2015 Chin. Phys. B 24 120401

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

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