Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

doi:10.1088/1674-1056/ad1dcb

中国物理B ›› 2024, Vol. 33 ›› Issue (5): 54501-054501.doi: 10.1088/1674-1056/ad1dcb

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

Shutian Zhang(张树甜), Shikun Liu(刘世鲲), Tengfei Jiao(矫滕菲), Min Sun(孙敏), Fenglan Hu(胡凤兰), and Decai Huang(黄德财)†

Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China

收稿日期:2023-10-27 修回日期:2024-01-04 接受日期:2024-01-12 出版日期:2024-05-20 发布日期:2024-05-20
通讯作者: Decai Huang E-mail:hdc@njust.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11574153) and the Foundation of the Ministry of Industry and Information Technology of China (Grant No. TSXK2022D007).

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

Shutian Zhang(张树甜), Shikun Liu(刘世鲲), Tengfei Jiao(矫滕菲), Min Sun(孙敏), Fenglan Hu(胡凤兰), and Decai Huang(黄德财)†

Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2023-10-27 Revised:2024-01-04 Accepted:2024-01-12 Online:2024-05-20 Published:2024-05-20
Contact: Decai Huang E-mail:hdc@njust.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11574153) and the Foundation of the Ministry of Industry and Information Technology of China (Grant No. TSXK2022D007).

摘要/Abstract

摘要： This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three stages (the pre-in-phase traveling stage, the central-collision stage, and the post-in-phase traveling stage) are identified to describe the nonlinear interaction processes in the granular chain. The nonlinear scattering effect occurs in the central-collision stage, which decreases the amplitude of the incident solitary waves. Compared with the leading-time phase in the incident and separation collision processes, the lagging-time phase in the separation collision process is smaller. This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage. We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain. The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude. The results are reversed in the fluid. An increase in solitary wave amplitude leads to decreased attachment, detachment, and residence times for granular chains and fluid. For the immediate time-phase shift, leading and lagging phenomena appear in the granular chain and the fluid, respectively. These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

关键词: integrable system, nonintegrable system, granular chain, solitary wave

Abstract: This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three stages (the pre-in-phase traveling stage, the central-collision stage, and the post-in-phase traveling stage) are identified to describe the nonlinear interaction processes in the granular chain. The nonlinear scattering effect occurs in the central-collision stage, which decreases the amplitude of the incident solitary waves. Compared with the leading-time phase in the incident and separation collision processes, the lagging-time phase in the separation collision process is smaller. This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage. We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain. The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude. The results are reversed in the fluid. An increase in solitary wave amplitude leads to decreased attachment, detachment, and residence times for granular chains and fluid. For the immediate time-phase shift, leading and lagging phenomena appear in the granular chain and the fluid, respectively. These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

Key words: integrable system, nonintegrable system, granular chain, solitary wave

中图分类号: (Granular systems)

45.70.-n

47.35.Fg (Solitary waves) 05.45.-a (Nonlinear dynamics and chaos) 04.60.Nc (Lattice and discrete methods)

Shutian Zhang(张树甜), Shikun Liu(刘世鲲), Tengfei Jiao(矫滕菲), Min Sun(孙敏), Fenglan Hu(胡凤兰), and Decai Huang(黄德财). Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems[J]. 中国物理B, 2024, 33(5): 54501-054501.

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Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

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