Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

doi:10.1088/1674-1056/26/12/120201

Abstract We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrödinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; (ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; (iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

Keywords: generalized Darboux transformation localized waves soliton rogue wave breather coupled cubic-quintic nonlinear Schrö dinger equations

Received: 05 July 2017
Revised: 12 August 2017
Accepted manuscript online:

PACS:	02.30.Ik	(Integrable systems)
	03.75.Nt	(Other Bose-Einstein condensation phenomena)
	31.15.-p	(Calculations and mathematical techniques in atomic and molecular physics)

Fund: Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11675054 and 11435005), the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014210140).

Corresponding Authors: Yong Chen
E-mail: ychen@sei.ecnu.edu.cn

Cite this article:

Tao Xu(徐涛), Yong Chen(陈勇), Ji Lin(林机) Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics 2017 Chin. Phys. B 26 120201

[1]	Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[2]	Hasegawa A and Kodama Y 1995 Solitons in Optical Communication (Oxford:Oxford University Press)
[3]	Ablowitz M J and Clarkson P A, 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge:Cambridge University Press)
[4]	Akhmediev N, Soto-Crespo J M and Ankiewicz A 2009 Phys. Rev. A 80 043818
[5]	Ohta Y and Yang J K 2012 Phys. Rev. E 86 036604
[6]	Dubard P and Matveev V B 2013 Nonlinearity 26 R93
[7]	Liu Y K and Li B 2017 Chin. Phys. Lett. 34 10202
[8]	Soto-Crespo J M, Devine N and Akhmediev N 2016 Phys. Rev. Lett. 116 103901
[9]	Chowdury A, Kedziora D J, Ankiewicz A and Akhmediev N 2015 Phys. Rev. E 91 022919
[10]	Forest M G, McLaughlin D W, Muraki D J and Wright O C 2000 J. Nonlinear Sci. 10 291
[11]	Ma Y C 1979 Stud. Appl. Math. 64 43
[12]	Akhmediev N and Korneev V I 1986 Theor. Math. Phys. 69 1089
[13]	Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675
[14]	Guo B L, Tian L X, Yan Z Y and Ling L M 2015 Rogue Waves and their Mathematical Theory (Hangzhou:Zhejiang Science and Technology Press)
[15]	Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 54
[16]	Akhmediev N, Dudley J M, Solli D R and Turitsyn S K 2013 J. Opt. 15 060201
[17]	Shats M, Punzmann H and Xia H 2010 Phys. Rev. Lett. 104 104503
[18]	Ganshin A N, Efimov V B, Kolmakov G V, Mezhov-Deglin L P and McClintock P V E 2008 Phys. Rev. Lett. 101 065303
[19]	Pitaevskii L and Stringari S 2016 Bose-Einstein Condensation and Superfluidity (Oxford:Oxford University Press)
[20]	Bailung H and Nakamura Y 1993 J. Plasma Phys. 50 231
[21]	Yan Z Y Phys. Lett. A 375 4274
[22]	Jia J and Lin J 2012 Opt. Express 20 7469
[23]	Ren B and Lin J 2015 Z. Naturforsch. A 70 539
[24]	Huang L L and Chen Y 2016 Chin. Phys. B 25 060201
[25]	Kedziora D J, Ankiewicz A and Akhmediev N 2014 Eur. Phys. J. Spec. Top. 223 43
[26]	Zhang X E and Chen Y 2017 Commun. Nonlinear Sci. Numer. Simul. 52 24
[27]	Zhang X E, Chen Y and Tang X Y arXiv:1610.09507v1
[28]	Wang L, Zhu Y J, Wang Z Z, Qi F H and Guo R 2016 Commun. Nonlinear Sci. Numer. Simul. 33 218
[29]	Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202
[30]	Wang X and Chen Y 2014 Chin. Phys. B 23 070203
[31]	Xu T and Chen Y 2016 Chin. Phys. B 25 090201
[32]	Wang X, Li Y Q and Chen Y 2014 Wave Motion 51 1149
[33]	Wang X, Yang B, Chen Y and Yang Y Q 2014 Chin. Phys. Lett. 31 090201
[34]	Zhao L C, Yang Z Y and Ling L M 2014 J. Phys. Soc. Jpn. 83 104401
[35]	Rao J G, Liu Y B, Qian C and He J S 2017 Z. Naturforsch. A 72
[36]	Wang P and Tian B 2012 Opt. Commun. 285 3567
[37]	Qi F H, Tian B, Lü X, Guo R and Xue Y S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2372
[38]	Zhang Y, Nie X J and Zha Q L 2014 Phys. Lett. A 378 191
[39]	Wang Y F, Tian B, Sun W R and Liu X R 2016 Optik 127 5750
[40]	Kundu A 1984 J. Math. Phys. 25 3433
[41]	Huang G Q and Lin J 2017 Acta Phys. Sin. 66 054208(in Chinese)
[42]	Geng X G 1999 Physica A 180 241
[43]	Geng X G and Tam H W 1999 J. Phys. Soc. Jpn. 68 1508
[44]	Zha Q L 2013 Phys. Lett. A 377 855
[45]	Wang X, Yang B, Chen Y and Yang Y Q 2014 Phys. Scr. 89 095210
[46]	Baronio F 2012 Phys. Rev. Lett. 109 044102
[47]	Matveev V B 1991 Darboux Transformations and Solitons (New York:Springer-Verlag)

[1]	Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations Feng Yuan(袁丰) and Behzad Ghanbari. Chin. Phys. B, 2023, 32(4): 040201.
[2]	Riemann--Hilbert approach of the complex Sharma—Tasso—Olver equation and its N-soliton solutions Sha Li(李莎), Tiecheng Xia(夏铁成), and Hanyu Wei(魏含玉). Chin. Phys. B, 2023, 32(4): 040203.
[3]	All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). Chin. Phys. B, 2023, 32(3): 030506.
[4]	Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Chin. Phys. B, 2023, 32(3): 030505.
[5]	Matrix integrable fifth-order mKdV equations and their soliton solutions Wen-Xiu Ma(马文秀). Chin. Phys. B, 2023, 32(2): 020201.
[6]	A cladding-pumping based power-scaled noise-like and dissipative soliton pulse fiber laser Zhiguo Lv(吕志国), Hao Teng(滕浩), and Zhiyi Wei(魏志义). Chin. Phys. B, 2023, 32(2): 024207.
[7]	Real-time observation of soliton pulsation in net normal-dispersion dissipative soliton fiber laser Xu-De Wang(汪徐德), Xu Geng(耿旭), Jie-Yu Pan(潘婕妤), Meng-Qiu Sun(孙梦秋), Meng-Xiang Lu(陆梦想), Kai-Xin Li(李凯芯), and Su-Wen Li(李素文). Chin. Phys. B, 2023, 32(2): 024210.
[8]	Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture Lei Chen(陈磊), Pan Li(李磐), He-Shan Liu(刘河山), Jin Yu(余锦), Chang-Jun Ke(柯常军), and Zi-Ren Luo(罗子人). Chin. Phys. B, 2023, 32(2): 024213.
[9]	Charge self-trapping in two strand biomolecules: Adiabatic polaron approach D Chevizovich, S Zdravković, A V Chizhov, and Z Ivić. Chin. Phys. B, 2023, 32(1): 010506.
[10]	Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Chin. Phys. B, 2023, 32(1): 010505.
[11]	Oscillation properties of matter-wave bright solitons in harmonic potentials Shu-Wen Guan(关淑文), Ling-Zheng Meng(孟令正), and Li-Chen Zhao(赵立臣). Chin. Phys. B, 2022, 31(8): 080506.
[12]	Gap solitons of spin-orbit-coupled Bose-Einstein condensates in $\mathcal{PT}$ periodic potential S Wang(王双), Y H Liu(刘元慧), and T F Xu(徐天赋). Chin. Phys. B, 2022, 31(7): 070306.
[13]	Spatio-spectral dynamics of soliton pulsation with breathing behavior in the anomalous dispersion fiber laser Ying Han(韩颖), Bo Gao(高博), Jiayu Huo(霍佳雨), Chunyang Ma(马春阳), Ge Wu(吴戈),Yingying Li(李莹莹), Bingkun Chen(陈炳焜), Yubin Guo(郭玉彬), and Lie Liu(刘列). Chin. Phys. B, 2022, 31(7): 074208.
[14]	Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉). Chin. Phys. B, 2022, 31(6): 060201.
[15]	Sequential generation of self-starting diverse operations in all-fiber laser based on thulium-doped fiber saturable absorber Pei Zhang(张沛), Kaharudin Dimyati, Bilal Nizamani, Mustafa M. Najm, and S. W. Harun. Chin. Phys. B, 2022, 31(6): 064204.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

Cite this article:

Online attention