Head-on collision between two solitary waves in a one-dimensional bead chain

doi:10.1088/1674-1056/27/4/044501

Abstract The head on collision between two opposite propagating solitary waves is studied in the present paper both numerically and analytically. The interesting result is that no phase shift is observed which is different from that found in other branches of physics. It is found that the maximum amplitude in the process of the head on collision is close to the linear sum of two colliding solitary waves.

Keywords: discrete system bead chain solitary waves

Received: 24 November 2017
Revised: 12 January 2018
Accepted manuscript online:

PACS:	45.05.+x	(General theory of classical mechanics of discrete systems)
	05.45.-a	(Nonlinear dynamics and chaos)
	45.70.-n	(Granular systems)

Fund: Project supported by the National Magnetic Confinement Fusion Science Program of China (Grant No. 2014GB104002), the National Natural Science Foundation of China (Grant No. 11647313), the Youth Science and Technology Foundation of Gansu Province, China (Grant No. 1606RJYA263), and the Institutes of Higher Education Institutions of Gansu Province, China (Grant No. 2015B-022).

Corresponding Authors: Wen-Shan Duan
E-mail: duanws@nwnu.edu.cn

Cite this article:

Fu-Gang Wang(王扶刚), Yang-Yang Yang(杨阳阳), Juan-Fang Han(韩娟芳), Wen-Shan Duan(段文山) Head-on collision between two solitary waves in a one-dimensional bead chain 2018 Chin. Phys. B 27 044501

[1]	Korteweg D J and Vries G D 1895 Philosophical Magazine 39 422
[2]	Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[3]	Nesterenko V F 1983 J. Appl. Mech. Tech. Phys. 24 733
[4]	Coste C, Falcon E and Fauve S 1997 Phys. Rev. E. 56 6104
[5]	Nesterenko V F 2001 Dynamics of Heterogeneous Materials (New York:Springer)
[6]	Lazaridi A N and Nesterenko V F 1985 J. Appl. Mech. Tech. Phys. 26 405
[7]	Su C H and Mirie R M 1980 J. Fluid Mech. 98 509
[8]	Gardner C S, Greene J M, Kruskal M D and Miura R M 1967 Phys. Rev. Lett. 19 1095
[9]	Huang G X and Velarde M G 1995 Phys. Rev. E 53 2988
[10]	Xu Y X, Liu Z M, Lin M M, Shi Y R, Chen J M and Duan W S 2011 Phys. Plasmas 18 052301
[11]	Han J N, Du S L and Duan W S 2008 Phys. Plasmas 15 112104
[12]	Li S C and Duan W S 2008 Eur. Phys. J. B 62 485
[13]	Zhang Y and Ding N 2008 Chin. Phys. B 17 2994
[14]	Nejoh Y 1992 Phys. Fluids B:Plasma Physics 4 2830
[15]	Sokolow A and Sen S 2005 Phys. Rev. Lett. 94 178002
[16]	Nesterenko V F, Daraio C, Herbold E B and Jin S 2005 Phys. Rev. Lett. 95 158702
[17]	Job S, Melo F, Sokolow A and Sen S 2007 Granular Matter 10 13
[18]	Harbola U, Rosas A, Romero A H, Esposito M and Lindenberg K 2009 Phys. Rev. E 80 051302
[19]	Harbola U, Rosas A, Romero A H and Lindenberg K 2010 Phys. Rev. E 82 011306
[20]	Melo F, Job S, Santibanez F and Tapia F 2006 Phys. Rev. E 73 041305
[21]	Doney R L 2005 Phys. Rev. E 72 041304
[22]	Boechler N, Theocharis G, Job S, Kevrekidis P G, Porter M A and Daraio C 2010 Phys. Rev. Lett. 104 244302
[23]	Theocharis G, Boechler N, Kevrekidis P G, Job S, Porter M A and Daraio C 2010 Phys. Rev. E 82 056604
[24]	Job S, Santibanez F, Tapia F and Melo F 2009 Phys. Rev. E 80 025602
[25]	Martinez A J, Yasuda H, Kim E, Kevrekidis P G, Porter M A and Yang J 2016 Phys. Rev. E 93 052224
[26]	Li F, Zhao L X, Tian Z H, Yu L Y and Yang J 2013 Smart Mater. Struct. 22 035016
[27]	Liu S W, Yang Y Y, Duan W S and Yang L 2015 Phys. Rev. E 92 013202
[28]	Shen Y, Kevrekidis P G, Sen S and Hoffman A 2014 Phys. Rev. E 90 022905
[29]	Qi X, Xu Y X, Duan W S, Zhang L Y and Yang L 2014 Phys. Plasmas 21 082118
[30]	Zhang J, Yang Y, Xu Y X, Yang L, Qi X and Duan W S 2014 Phys. Plasmas 21 103706
[31]	Jaiswal S, Bandyopadhyay P and Sen A 2014 Phys. Plasmas 21 053701
[32]	Roy K, Chatterjee P and Roychoudhury R 2014 Phys. Plasmas 21 104509
[33]	Maxworthy T 1976 J. Fluid Mech. 76 177
[34]	Sharma S K, Boruah A and Bailung H 2014 Phys. Rev. E 89 013110
[35]	Santibanez F, Munoz R, Caussarieu A, Job S and Melo F 2011 Phys. Rev. E 84 026604
[36]	Hinch E J and Saint-Jean S 1999 Proc. R. Soc. Lond. A 455 3201
[37]	Spence D A 1968 Proc. Roy. Soc. A 305 55
[38]	Leblond H 2008 J. Phys. B:At. Mol. Opt. Phys. 41 043001
[39]	Taniuti T and WEI C C 1968 J. Phys. Soc. Jpn. 24 941
[40]	Yang Y Y, Liu S W, Yang Q, Zhang Z B, Duan W S and Yang L 2016 AIP Adv. 6 075317
[41]	Takato Y and Sen S 2012 Europhys. Lett. 100 24003

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Head-on collision between two solitary waves in a one-dimensional bead chain

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