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

doi:10.1088/1674-1056/ab50fc

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.

Keywords: dark soliton three-component nonlinear Schrödinger equations general nonzero background

Received: 29 August 2019
Revised: 09 October 2019
Accepted manuscript online:

PACS:	02.30.Ik	(Integrable systems)
	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)

Fund: 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).

Corresponding Authors: Liming Ling
E-mail: linglm@scut.edu.cn

Cite this article:

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 2019 Chin. Phys. B 28 120201

[34]	Zhang H Q and Wang Y 2018 Nonlinear Dyn. 91 1921
[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
[2]	Zhang Y, Nie X J and Zha Q L 2014 Phys. Lett. A 378 191
[3]	Kurihara S 1981 Phys. B+C 107 413
[4]	Du Z, Tian B, Chai H P and Yuan Y Q 2019 Commun. Nonlinear Sci. Numer. Simul. 67 49
[5]	Zhao L C, Yang Z Y and Yang W L 2019 Chin. Phys. B 28 010501
[6]	Liu Y K, Li B 2017 Chin. Phys. Lett. 34 010202
[7]	Wang X B and Han B 2019 Europhys. Lett. 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
[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
[10]	Wang Z H, Cherkasskii M, Kalinikos B A, Carr L D and Wu M Z 2014 New J. Phys. 16 053048
[11]	Guo B L and Wang Y F 2016 Wave Motion 67 47
[12]	Li H, Wang D N and Cheng Y S 2009 Chaos Solitons Fractals 39 1988
[13]	Liu X X, Pu H, Xiong B, Liu W M and Gong J B 2009 Phys. Rev. A 79 013423
[14]	Ling L M and Zhao L C 2015 Phys. Rev. E 92 022924
[15]	Qu C L, Pitaevskii L P and Stringari S 2016 Phys. Rev. Lett. 116 160402
[16]	Yu W T, Ekici M, Mirzazadeh M, Zhou Q, Liu W J 2018 Optik 165 341
[17]	Frantzeskakis D J 2010 J. Phys. A: Math. Theor. 43 213001
[18]	Ohta Y, Wang D S and Yang J K 2011 Stud. Appl. Math. 127 345
[19]	Mahalingam A and Porsezian K 2001 Phys. Rev. E 64 046608
[20]	Priya N V and Senthilvelan M 2016 Commun. Nonlinear Sci. Numer. Simul. 36 366
[21]	Ling L M, Zhao L C and Guo B L 2015 Nonlinearity 28 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
[25]	Gadzhimuradov T A, Abdullaev G O and Agalarov A M 2017 Nonlinear Dyn. 89 2695
[26]	Huang Q M 2019 Appl. Math. Lett. 93 29
[27]	Su J J and Gao Y T 2017 Superlattices Microstruct. 104 498
[28]	Lan Z Z, Gao B and Du M J 2018 Chaos Solitons Fractals. 111 169
[29]	Li L, Zhao X S and Xu Z Y 2008 Phys. Rev. A 78 063833
[30]	Shin H J 2005 J. Phys. A: Math. Gen. 38 3307
[31]	Lan Y, Zhao L C and Luo X W 2019 Commun. Nonlinear Sci. Numer. Simul. 70 334
[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
[34]	Zhang H Q and Wang Y 2018 Nonlinear Dyn. 91 1921
[35]	Zhang H Q and Yuan S S 2017 Commun. Nonlinear Sci. Numer. Simul. 51 124

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

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