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

doi:10.1088/1674-1056/ad1dcb

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.

Keywords: integrable system nonintegrable system granular chain solitary wave

Received: 27 October 2023
Revised: 04 January 2024
Accepted manuscript online: 12 January 2024

PACS:	45.70.-n	(Granular systems)
	47.35.Fg	(Solitary waves)
	05.45.-a	(Nonlinear dynamics and chaos)
	04.60.Nc	(Lattice and discrete methods)

Fund: 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).

Corresponding Authors: Decai Huang
E-mail: hdc@njust.edu.cn

Cite this article:

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 2024 Chin. Phys. B 33 054501

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

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