Chin. Phys. Lett.  2020, Vol. 37 Issue (3): 030501    DOI: 10.1088/0256-307X/37/3/030501
GENERAL |
Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schrödinger Equation
Bao Wang1, Zhao Zhang2, Biao Li2**
1Robotics Institute, Ningbo University of Technology, Ningbo 315211
2School of Mathematics and Statistics, Ningbo University, Ningbo 315211
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Bao Wang, Zhao Zhang, Biao Li 2020 Chin. Phys. Lett. 37 030501
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Abstract Based on velocity resonance and Darboux transformation, soliton molecules and hybrid solutions consisting of soliton molecules and smooth positons are derived. Two new interesting results are obtained: the first is that the relationship between soliton molecules and smooth positons is clearly pointed out, and the second is that we find two different interactions between smooth positons called strong interaction and weak interaction, respectively. The strong interaction will only disappear when $t \to \infty$. This strong interaction can also excite some periodic phenomena.
Received: 29 December 2019      Published: 22 February 2020
PACS:  05.45.Yv (Solitons)  
  02.30.Ik (Integrable systems)  
  47.20.Ky (Nonlinearity, bifurcation, and symmetry breaking)  
  52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos. 11775121, Department of Education of Zhejiang Province under Grant No. Y201839043 and the K.C. Wong Magna Fund in Ningbo University.
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http://cpl.iphy.ac.cn/10.1088/0256-307X/37/3/030501       OR      http://cpl.iphy.ac.cn/Y2020/V37/I3/030501
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Bao Wang
Zhao Zhang
Biao Li
[1]He J S, Zhang H R, Wang L H, Porsezian K and Fokas A S 2013 Phys. Rev. E 87 052914
[2]He J S, Wang L H, Li L J, Porsezian K and Erdélyi R 2014 Phys. Rev. E 89 062917
[3]Wang L H, He J S, Xu H, Wang J and Porsezian K 2017 Phys. Rev. E 95 042217
[4]He J S, Zhang L, Cheng Y and Li Y S 2006 Sci. Chin. Ser. A: Math. 49 1867 DOI: 10.1007/s11425-006-2025
[5]Lakomy K, Nath R and Santos L 2012 Phys. Rev. A 85 033618
[6]Herink G, Kurtz F, Jalali B, Solli D R and Ropers C 2017 Science 356 50
[7]Liu X M, Yao X K and Cui Y D 2018 Phys. Rev. Lett. 121 023905
[8]Lou S Y 2019 arXiv:1909.03399
[9]Zhang Z, Yang S X and Li B 2019 Chin. Phys. Lett. 36 120501
[10]Zhang Z, Yang X Y and Li B 2020 Appl. Math. Lett. 103 106168
[11]Zhang Y S, Guo L J, He J S and Zhou Z X 2015 Lett. Math. Phys. 105 853
[12]Qiu D Q and Cheng W G 2019 Appl. Math. Lett. 98 13
[13]Liu W, Zhang Y S and He J S 2018 Waves Random Complex Media 28 203
[14]Song W J, Xu S W, Li M H and He J S 2019 Nonlinear Dyn. 97 2135
[15]Zhang Z, Yang X Y, Li W T and Li B 2019 Chin. Phys. B 28 110201
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