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Chin. Phys. B, 2022, Vol. 31(1): 010201    DOI: 10.1088/1674-1056/ac0907
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Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance

Hongcai Ma(马红彩)1,2,†, Yuxin Wang(王玉鑫)1,‡, and Aiping Deng(邓爱平)1,2
1 Department of Applied Mathematics, Donghua University, Shanghai 201620, China;
2 Institute for Nonlinear Sciences, Donghua University, Shanghai 201620, China
Abstract  We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation. What is more, each soliton molecule can be transformed into an asymmetric soliton by changing the parameter φ. In addition, the collision between soliton molecules (or asymmetric soliton) and several soliton solutions is observed. Finally, some related pictures are presented.
Keywords:  the extended Lax equation      soliton molecules      velocity resonance mechanism  
Received:  28 April 2021      Revised:  19 May 2021      Accepted manuscript online:  08 June 2021
PACS:  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
  04.30.Nk (Wave propagation and interactions)  
  04.20.Jb (Exact solutions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11371086, 11671258, and 11975145), the Fund of Science and Technology Commission of Shanghai Municipality, China (Grant No. 13ZR1400100), the Fund of Institute for Nonlinear Sciences, Donghua University, and the Fundamental Research Funds for the Central Universities, China (Grant No. 2232021G-13).
Corresponding Authors:  Hongcai Ma, Yuxin Wang     E-mail:  hongcaima@hotmail.com;wangyuxin0130@163.com

Cite this article: 

Hongcai Ma(马红彩), Yuxin Wang(王玉鑫), and Aiping Deng(邓爱平) Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance 2022 Chin. Phys. B 31 010201

[1] Akhmediev N and Ankiewicz A 2000 Chaos 10 600
[2] Stratmann M, Pagel T and Mitschke F 2005 Phys. Rev. Lett. 95 143902
[3] Herink G, Kurtz F, Jalali B, Solli D R and Ropers C 2017 Science 356 50
[4] Liu X M, Yao X K and Cui Y D 2018 Phys. Rev. Lett. 121 23905
[5] Kazimierz L, Rejish N and Luis S 2012 Phys. Rev. A 86 013610
[6] Katarzyna K, Nithyanandan K, Ugo A, Patrice T and Philippe G 2017 Phys. Rev. Lett. 118 243901
[7] Dudley M J, Dias F, Erkintalo M and Genty G 2014 Nat. Photon. 8 755
[8] Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[9] Kivshar Y S, Malomed B A and Shirshov P P 1989 Phys. Rev. Lett. 61 763
[10] Thomas H and Horowitz G T 2005 Phys. Rev. Lett. 94 221301
[11] Rohrmann P, Hause A and Mitschke F 2013 Phys. Rev. A 87 043834
[12] Lou S Y 2020 J. Phys. Commun. 4 041002
[13] Xu D H and Lou S Y 2020 Acta Phys. Sin. 69 014208 (in Chinese)
[14] Zhang Z, Yang S X and Li B 2019 Chin. Phys. Lett. 36 120501
[15] Yan Z W and Lou S Y 2020 Appl. Math. Lett. 104 106271
[16] Yang X Y, Fan R and Li B 2020 Phys. Scr. 95 045213
[17] Yang X Y, Zhang Z and Li B 2020 Chin. Phys. B. 29 100501
[18] Dong J J, Li B and Yuen M 2020 Commun. Theor. Phys. 72 025002
[19] Ma H C, Cheng Q X and Deng A P 2020 Commun. Theor. Phys. 72 095001
[20] Ma H C, Cheng Q X and Deng A P 2021 Mod. Phys. Lett. B 35 2150174
[21] Ma W X 2021 Int. J. Nonlinear Sci. Numer. Simul. 22 000010151520200214
[22] Ma W X 2021 Opt. Quantum Electron. 52 511
[23] Ma W X 2021 J. Geometry Phys. 165 104191
[24] Wazwaz A M 2016 J. Ocean Eng. Sci. 1 181
[25] Marchant T R and Smyth N F 1990 J. Fluid Mech. 221 263
[26] Marchant T R and Smyth N F 1996 IMA J. Appl. Math. 56 157
[27] Dullin H R, Gottwald G A and Holm D D 2003 Fluid Dyn. Res. 33 73
[28] Dullin H R, Gottwald G A and Holm D D 2004 Physica D 190 1
[29] Wang L, Zhu Y J, Wang Z Z, Qi F H and Guo R 2016 Commun. Nonlinear Sci. Numer. Simul. 33 218
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