Decaying solitary waves propagating in one-dimensional damped granular chain

doi:10.1088/1674-1056/27/7/074501

Abstract We numerically investigate the nonlinear waves propagating in a one-dimensional particle chain when the damping effect is taken into account. It is found that decaying solitary waves exist, in which the amplitude of the wave decreases exponentially as time increases. Meanwhile, the velocity of the solitary wave also slows down as time goes. This result implies that the damping coefficient is an important parameter in such a nonlinear system. Theoretical analysis has also been done by the reductive perturbation method. The result indicates that the nonlinear waves propagating in such a system can be described by the damped KdV equation.

Keywords: damping granular chain solitary wave damped KdV equation

Received: 19 October 2017
Revised: 21 March 2018
Accepted manuscript online:

PACS:	45.05.+x	(General theory of classical mechanics of discrete systems)
	05.45.-a	(Nonlinear dynamics and chaos)
	46.40.Cd	(Mechanical wave propagation (including diffraction, scattering, and dispersion))
	45.70.-n	(Granular systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.11565021 and 11047010) and the Scientific Research Foundation of Northwest Normal University, China (Grant No. NWNU-LKQN-16-3).

Corresponding Authors: Yuren Shi
E-mail: shiyr@nwnu.edu.cn

Cite this article:

Zongbin Song(宋宗斌), Xueying Yang(杨雪滢), Wenxing Feng(封文星), Zhonghong Xi(席忠红), Liejuan Li(李烈娟), Yuren Shi(石玉仁) Decaying solitary waves propagating in one-dimensional damped granular chain 2018 Chin. Phys. B 27 074501

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Decaying solitary waves propagating in one-dimensional damped granular chain

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