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
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

[1] Osborne A R and Burch T L 1980 Science 208 451
[2] Shukla P K, Yu M Y, and Tsintsadze N L 1984 Phys. Fluids 27 327
[3] Shukla N and Shukla P K 2007 Phys. Lett. A 367 120
[4] Schwarz U T, English L Q and Sievers A J 1999 Phys. Rev. Lett. 83 223
[5] Xie A H, van der Meer L, Hoff W and Austin R H 2000 Phys. Rev. Lett. 84 5435
[6] Fleischer J W, Segev M, Efremidis N K and Christodoulides D N 2003 Nature 422 147
[7] Sen S, Hong J, Bang J, Avalos E and Doney R 2008 Phys. Rep. 462 21
[8] Rosas A and Lindenberg K 2018 Phys. Rep. 735 1
[9] Korteweg D J and de Vries G 2011 Philos. Mag. 91 1007
[10] Nesterenko V F 1983 J. Appl. Mech. Tech. Phys. 24 733
[11] Nesterenko V F 2018 Phil. Trans. R. Soc. A 376 20170130
[12] Fermi E, Pasta J and Ulam S 1974 Lect. Appl. Math. 15 143
[13] Vainchtein A 2022 Phys. D 434 133252
[14] Nesterenko V F 2001 Dynamics of Heterogeneous Materials (New York:Springer-Verlag) pp. 17-20
[15] Sen S, Manciu M and Wright J D 1998 Phys. Rev. E 57 2386
[16] Sen S and Manciu M 1999 Phys. A 268 644
[17] Manciu M, Sen S and Hurd A J 1999 Phys. A 274 588
[18] Chong C, Porter M A, Kevrekidis P G and Daraio C 2017 J. Phys.:Condens. Matter 29 413003
[19] Manciu M, Sen S and Hurd A J 2000 Phys. Rev. E 63 016614
[20] Manciu F S and Sen S 2002 Phys. Rev. E 66 016616
[21] Avalos E and Sen S 2009 Phys. Rev. E 79 046607
[22] Wen Z Y, Wang S J, Zhang X M and Lei L 2007 Chin. Phys. Lett. 24 2887
[23] Santibanez F, Munoz R, Caussarieu A, Job S and Melo F 2011 Phys. Rev. E 84 026604
[24] Shen Y, Kevrekidis P G, Sen S and Hoffman A 2014 Phys. Rev. E 90 022905
[25] Wang F G, Yang Y Y, Han J F and Duan W S 2018 Chin. Phys. B 27 044501
[26] Wu Q Q, Liu X Y, Jiao T F, Sen S and Huang D C 2020 Chin. Phys. Lett. 37 074501
[27] Zhang W and Xu J 2021 Int. J. Mech. Sci. 191 106073
[28] Tichler A M, Gomez L R, Upadhyaya N, Campman X, Nesterenko V F and Vitelli V 2013 Phys. Rev. Lett. 111 048001
[29] Liu S W, Yang Y Y, Duan W S and Yang L 2015 Phys. Rev. E 92 013202
[30] Du W Q, Yang Y Y, Han J F and Duan W S 2020 Indian J. Phys. 94 1249
[31] Yang Y Y, Liu S W, Yang Q, Zhang Z B, Duan W S and Yang L 2016 AIP Advances 6 075317
[32] Su C H and Mirie R M 1980 J. Fluid Mech. 98 509
[33] Chen Y S and Yeh H 2014 J. Fluid Mech. 749 577
[34] Tong C, Shao Y L, Hanssen F C W, Li Y, Xie B and Lin Z L 2019 Wave Motion 88 34
[35] Chambarel J, Kharif C and Touboul J 2009 Nonlin. Processes Geophys. 16 111
[36] Deng G, Biondini G and Sen S 2020 Chaos 30 043101
[37] Maxworthy T 1976 J. Fluid Mech. 76 177
[38] Fenton J D and Rienecker M M 1982 J. Fluid Mech. 118 411
[39] Power H and Chwang A T 1984 Wave Motion 6 183
[40] Byatt-Smith J G B 1988 J. Fluid Mech. 197 503
[41] Cooker M J, Weidman P D and Bale D S 1997 J. Fluid Mech. 342 141
[42] Chen Y Y, Kharif C, Yang J H, Hsu H C, Touboul J and Chambarel J 2015 Eur. J. Mech. B Fluid. 49 20
[43] Zhang J, Yang Y, Xu Y X, Yang L, Qi X and Duan W S 2014 Phys. Plasmas 21 103706
[44] Qi X, Xu Y X, Duan W S, Zhang L Y and Yang L 2014 Phys. Plasmas 21 082118
[45] Zhang J, Qi X, Zhang H and Duan W S 2016 Chin. Phys. Lett. 33 065202
[46] Landau L D and Lifshitz E M 2011 Theory of Elasticity (5th edn.) (Beijing:Higher Education Press) pp. 30-35
[47] Daraio C, Nesterenko V F, Herbold E B and Jin S 2005 Phys. Rev. E 72 016603
[48] Nesterenko V F 1994 J. Phys. IV 4 C8-729
[49] Nesterenko V F, Lazaridi A N and Sibiryakov E B 1995 J. Appl. Mech. Tech. Ph+ 36 166
[50] Daraio C, Nesterenko V F and Jin S 2004 AIP Conf. Proc. 706 197
[51] Job S, Melo F, Sokolow A and Sen S 2007 Granular Matter 10 13
[52] Byatt-Smith J G B 1971 J. Fluid Mech. 49 625
[53] Whitham G B 2016 Linear and Nonlinear Waves (Beijing:Science Press) pp. 438-444
[54] Craig W, Guyenne P, Hammack J, Henderson D and Sulem C 2006 Phys. Fluids 18 057106

[1]	Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton Qiao-Hong Han(韩巧红) and Man Jia(贾曼). Chin. Phys. B, 2024, 33(4): 040202.
[2]	Reconstructions of time-evolving sound-speed fields perturbed by deformed and dispersive internal solitary waves in shallow water Qin-Ran Li(李沁然), Chao Sun(孙超), Lei Xie(谢磊), and Xiao-Dong Huang(黄晓冬). Chin. Phys. B, 2023, 32(12): 124701.
[3]	Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network Sedric Ndoungalah, Guy Roger Deffo, Arnaud Djine, and Serge Bruno Yamgoué. Chin. Phys. B, 2023, 32(11): 110505.
[4]	Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields Jia-Sheng Dong(董家生), Pengcheng Lu(路鹏程), Pei Sun(孙佩), Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), Kun Hao(郝昆), and Wen-Li Yang(杨文力). Chin. Phys. B, 2023, 32(1): 017501.
[5]	Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯). Chin. Phys. B, 2022, 31(8): 080202.
[6]	Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation Bin He(何斌) and Qing Meng(蒙清). Chin. Phys. B, 2021, 30(6): 060201.
[7]	Particle-in-cell simulation of ion-acoustic solitary waves in a bounded plasma Lin Wei(位琳), Bo Liu(刘博), Fang-Ping Wang(王芳平), Heng Zhang(张恒), and Wen-Shan Duan(段文山). Chin. Phys. B, 2021, 30(3): 035201.
[8]	Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas Rong-An Tang(唐荣安), Tiao-Fang Liu(刘调芳), Xue-Ren Hong(洪学仁), Ji-Ming Gao(高吉明), Rui-Jin Cheng(程瑞锦), You-Lian Zheng(郑有莲), and Ju-Kui Xue(薛具奎). Chin. Phys. B, 2021, 30(1): 015201.
[9]	On superintegrable systems with a position-dependent mass in polar-like coordinates Hai Zhang(章海)†. Chin. Phys. B, 2020, 29(10): 100201.
[10]	Exact transverse solitary and periodic wave solutions in a coupled nonlinear inductor-capacitor network Serge Bruno Yamgoué, Guy Roger Deffo, Eric Tala-Tebue, François Beceau Pelap. Chin. Phys. B, 2018, 27(9): 096301.
[11]	Decaying solitary waves propagating in one-dimensional damped granular chain 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). Chin. Phys. B, 2018, 27(7): 074501.
[12]	Nucleus-acoustic solitary waves in self-gravitating degenerate quantum plasmas D M S Zaman, M Amina, P R Dip, A A Mamun. Chin. Phys. B, 2018, 27(4): 040402.
[13]	Head-on collision between two solitary waves in a one-dimensional bead chain Fu-Gang Wang(王扶刚), Yang-Yang Yang(杨阳阳), Juan-Fang Han(韩娟芳), Wen-Shan Duan(段文山). Chin. Phys. B, 2018, 27(4): 044501.
[14]	Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays Li-Yuan Ma(马立媛), Jia-Liang Ji(季佳梁), Zong-Wei Xu(徐宗玮), Zuo-Nong Zhu(朱佐农). Chin. Phys. B, 2018, 27(3): 030201.
[15]	Envelope solitary waves and their reflection and transmission due to impurities in a granular material Wen-Qing Du(杜文青), Jian-An Sun(孙建安), Yang-Yang Yang(杨阳阳), Wen-Shan Duan(段文山). Chin. Phys. B, 2018, 27(1): 014501.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention