Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

doi:10.1088/1674-1056/ab50fc

中国物理B ›› 2019, Vol. 28 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/ab50fc

• GENERAL • 下一篇

Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

Zhi-Jin Xiong(熊志进), Qing Xu(许庆), Liming Ling(凌黎明)

1 School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China;
2 School of Mathematics, South China University of Technology, Guangzhou 510640, China

收稿日期:2019-08-29 修回日期:2019-10-09 出版日期:2019-12-05 发布日期:2019-12-05
通讯作者: Liming Ling E-mail:linglm@scut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11771151), the Guangdong Natural Science Foundation of China (Grant No. 2017A030313008), the Guangzhou Science and Technology Program of China (Grant No. 201904010362), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2019MS110).

Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

Zhi-Jin Xiong(熊志进)¹, Qing Xu(许庆)², Liming Ling(凌黎明)²

1 School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China;
2 School of Mathematics, South China University of Technology, Guangzhou 510640, China

Received:2019-08-29 Revised:2019-10-09 Online:2019-12-05 Published:2019-12-05
Contact: Liming Ling E-mail:linglm@scut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11771151), the Guangdong Natural Science Foundation of China (Grant No. 2017A030313008), the Guangzhou Science and Technology Program of China (Grant No. 201904010362), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2019MS110).

摘要/Abstract

摘要： We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrödinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrödinger systems, and require more in-depth studies in the future.

关键词: dark soliton, three-component nonlinear Schrödinger equations, general nonzero background

Abstract: We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrödinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrödinger systems, and require more in-depth studies in the future.

Key words: dark soliton, three-component nonlinear Schrödinger equations, general nonzero background

中图分类号: (Integrable systems)

02.30.Ik

03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 42.81.Dp (Propagation, scattering, and losses; solitons)

熊志进, 许庆, 凌黎明. Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background[J]. 中国物理B, 2019, 28(12): 120201-120201.

Zhi-Jin Xiong(熊志进), Qing Xu(许庆), Liming Ling(凌黎明). Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background[J]. Chin. Phys. B, 2019, 28(12): 120201-120201.

参考文献 35

[34]	Zhang H Q and Wang Y 2018 Nonlinear Dyn. 91 1921 doi: 10.1007/s11071-017-3990-3
[1]	Gerdjikov V S 2009 AIP Conf. Proc. 1186 15
[35]	Zhang H Q and Yuan S S 2017 Commun. Nonlinear Sci. Numer. Simul. 51 124 doi: 10.1016/j.cnsns.2017.03.019
[2]	Zhang Y, Nie X J and Zha Q L 2014 Phys. Lett. A 378 191 doi: 10.1016/j.physleta.2013.11.010
[3]	Kurihara S 1981 Phys. B+C 107 413 doi: 10.1016/0378-4363(81)90512-X
[4]	Du Z, Tian B, Chai H P and Yuan Y Q 2019 Commun. Nonlinear Sci. Numer. Simul. 67 49 doi: 10.1016/j.cnsns.2018.06.014
[5]	Zhao L C, Yang Z Y and Yang W L 2019 Chin. Phys. B 28 010501 doi: 10.1088/1674-1056/28/1/010501
[6]	Liu Y K, Li B 2017 Chin. Phys. Lett. 34 010202 doi: 10.1088/0256-307X/34/1/010202
[7]	Wang X B and Han B 2019 Europhys. Lett. 126 15001 doi: 10.1209/0295-5075/126/15001
[8]	Zhao L C, Ling L M, Qi J W, Yang Z Y and Yang W L 2017 Commun. Nonlinear Sci. Numer. Simul. 49 39 doi: 10.1016/j.cnsns.2017.02.004
[9]	Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K, Sanpera A, Shlyapnikov G V and Lewenstein M 1999 Phys. Rev. Lett. 83 5198 doi: 10.1103/PhysRevLett.83.5198
[10]	Wang Z H, Cherkasskii M, Kalinikos B A, Carr L D and Wu M Z 2014 New J. Phys. 16 053048 doi: 10.1088/1367-2630/16/5/053048
[11]	Guo B L and Wang Y F 2016 Wave Motion 67 47 doi: 10.1016/j.wavemoti.2016.06.013
[12]	Li H, Wang D N and Cheng Y S 2009 Chaos Solitons Fractals 39 1988 doi: 10.1016/j.chaos.2007.06.063
[13]	Liu X X, Pu H, Xiong B, Liu W M and Gong J B 2009 Phys. Rev. A 79 013423 doi: 10.1103/PhysRevA.79.013423
[14]	Ling L M and Zhao L C 2015 Phys. Rev. E 92 022924 doi: 10.1103/PhysRevE.92.022924
[15]	Qu C L, Pitaevskii L P and Stringari S 2016 Phys. Rev. Lett. 116 160402 doi: 10.1103/PhysRevLett.116.160402
[16]	Yu W T, Ekici M, Mirzazadeh M, Zhou Q, Liu W J 2018 Optik 165 341 doi: 10.1016/j.ijleo.2018.03.137
[17]	Frantzeskakis D J 2010 J. Phys. A: Math. Theor. 43 213001 doi: 10.1088/1751-8113/43/21/213001
[18]	Ohta Y, Wang D S and Yang J K 2011 Stud. Appl. Math. 127 345 doi: 10.1111/j.1467-9590.2011.00525.x
[19]	Mahalingam A and Porsezian K 2001 Phys. Rev. E 64 046608 doi: 10.1103/PhysRevE.64.046608
[20]	Priya N V and Senthilvelan M 2016 Commun. Nonlinear Sci. Numer. Simul. 36 366 doi: 10.1016/j.cnsns.2015.12.016
[21]	Ling L M, Zhao L C and Guo B L 2015 Nonlinearity 28 3243 doi: 10.1088/0951-7715/28/9/3243
[22]	Conforti M, Baronio F and Degasperis A 2011 Physica D: Nonlinear Phenomena240 1362
[23]	Li S Q 2012 Third Global Congress on Intelligent Systems (Wuhan, China 6-8 November 2012) p. 352
[24]	Zhao X S, Li L and Xu Z Y 2009 Phys. Rev. A 79 043827 doi: 10.1103/PhysRevA.79.043827
[25]	Gadzhimuradov T A, Abdullaev G O and Agalarov A M 2017 Nonlinear Dyn. 89 2695 doi: 10.1007/s11071-017-3618-7
[26]	Huang Q M 2019 Appl. Math. Lett. 93 29 doi: 10.1016/j.aml.2019.01.029
[27]	Su J J and Gao Y T 2017 Superlattices Microstruct. 104 498 doi: 10.1016/j.spmi.2016.12.056
[28]	Lan Z Z, Gao B and Du M J 2018 Chaos Solitons Fractals. 111 169 doi: 10.1016/j.chaos.2018.04.005
[29]	Li L, Zhao X S and Xu Z Y 2008 Phys. Rev. A 78 063833 doi: 10.1103/PhysRevA.78.063833
[30]	Shin H J 2005 J. Phys. A: Math. Gen. 38 3307 doi: 10.1088/0305-4470/38/15/006
[31]	Lan Y, Zhao L C and Luo X W 2019 Commun. Nonlinear Sci. Numer. Simul. 70 334 doi: 10.1016/j.cnsns.2018.09.010
[32]	Matveev V B 2007 Philos. Trans.: Math. Phys. Eng. Sci. 366 837
[33]	Zhao L C and Ling L M 2016 J. Opt. Soc. Am. B 33 850 doi: 10.1364/JOSAB.33.000850
[34]	Zhang H Q and Wang Y 2018 Nonlinear Dyn. 91 1921 doi: 10.1007/s11071-017-3990-3
[35]	Zhang H Q and Yuan S S 2017 Commun. Nonlinear Sci. Numer. Simul. 51 124 doi: 10.1016/j.cnsns.2017.03.019

Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

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