Soliton Solutions to the Coupled Gerdjikov–Ivanov Equation with Rogue-Wave-Like Phenomena

doi:10.1088/0256-307X/34/9/090201

Chin. Phys. Lett.

2017, Vol. 34

Issue (9): 090201 DOI: 10.1088/0256-307X/34/9/090201

GENERAL

Soliton Solutions to the Coupled Gerdjikov–Ivanov Equation with Rogue-Wave-Like Phenomena

Jian-Bing Zhang^1**, Ying-Yin Gongye¹, Shou-Ting Chen²

¹School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116
²School of Mathematics and Physical Science, Xuzhou Institute of Technology, Xuzhou 221008

Cite this article:

Jian-Bing Zhang, Ying-Yin Gongye, Shou-Ting Chen 2017 Chin. Phys. Lett. 34 090201

Download: PDF(2056KB) PDF(mobile)(2059KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract Bilinear forms of the coupled Gerdjikov–Ivanov equation are derived. The $N$-soliton solutions to the equation are obtained by Hirota's method. It is interesting that the two-soliton solutions can generate the rogue-wave-like phenomena by selecting special parameters. The equation can be reduced to the Gerdjikov–Ivanov equation as well as its bilinear forms and its solutions.

Received: 18 April 2017 Published: 15 August 2017

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11671177 and 11271168, the Jiangsu Qing Lan Project (2014), and the Six Talent Peaks Project of Jiangsu Province under Grant No 2016-JY-08.

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/34/9/090201 OR https://cpl.iphy.ac.cn/Y2017/V34/I9/090201

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	Jian-Bing Zhang
	Ying-Yin Gongye
	Shou-Ting Chen

[1]	Johnson R S 1977 Proc. R. Soc. Lond. Ser. A 357 131
[2]	Kodama Y 1985 J. Stat. Phys. 39 597
[3]	Clarkson P A and Tuszynski J A 1990 J. Phys. A 23 4269
[4]	Kaup D J and Newell A C 1978 J. Math. Phys. 19 798
[5]	Chen H H, Lee Y C and Liu C S 1979 Phys. Scr. 20 490
[6]	Kakei S, Sasa N and Satsuma J 1995 J. Phys. Soc. Jpn. 64 1519
[7]	Gerdjikov V S and Ivanov M I 1983 Bull. J. Phys. 10 130
[8]	Kundu A 1987 Physica D 25 399
[9]	Clarkson P A and Cosgrove C M 1987 J. Phys. A 20 2003
[10]	Zhang J B, Chen S T and Li Q 2013 Phys. Scr. 88 065006
[11]	Zhang J B, Zhang D J and Shen Q 2011 Appl. Math. Comput. 218 4494
[12]	Zhang J B, Zhang D J and Chen D Y 2010 Commun. Theor. Phys. 53 211
[13]	Fan E G 2000 J. Math. Phys. 41 7769
[14]	Yu J, He J S and Han J W 2012 J. Math. Phys. 53 033708
[15]	Fan E G 2000 J. Phys. A 33 6925
[16]	Fan E G 2001 Commun. Theor. Phys. 35 651
[17]	Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202
[18]	Qian C, Rao J G, Liu Y B and He J S 2016 Chin. Phys. Lett. 33 110201
[19]	Xu S W and He J S 2012 J. Math. Phys. 53 063507
[20]	Guo L et al 2014 Phys. Scr. 89 035501
[21]	Dai H H and Fan E G 2004 Chaos Solitons & Fractals 22 93
[22]	Hou Y, Fan E G and Zhao P 2013 J. Math. Phys. 54 073505
[23]	Takahashi M and Konno K 1989 J. Phys. Soc. Jpn. 58 3505
[24]	Zhou J, Zhang D J and Zhao S L 2009 Phys. Lett. A 373 3248

Related articles from Frontiers Journals

[1]	S. Y. Lou, Man Jia, and Xia-Zhi Hao. Higher Dimensional Camassa–Holm Equations[J]. Chin. Phys. Lett., 2023, 40(2): 090201
[2]	Wen-Xiu Ma. Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions[J]. Chin. Phys. Lett., 2022, 39(10): 090201
[3]	Chong Liu, Shao-Chun Chen, Xiankun Yao, and Nail Akhmediev. Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations[J]. Chin. Phys. Lett., 2022, 39(9): 090201
[4]	Xiao-Man Zhang, Yan-Hong Qin, Li-Ming Ling, and Li-Chen Zhao. Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation[J]. Chin. Phys. Lett., 2021, 38(9): 090201
[5]	Kai-Hua Yin, Xue-Ping Cheng, and Ji Lin. Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation[J]. Chin. Phys. Lett., 2021, 38(8): 090201
[6]	Yusong Cao and Junpeng Cao. Exact Solution of a Non-Hermitian Generalized Rabi Model[J]. Chin. Phys. Lett., 2021, 38(8): 090201
[7]	Zequn Qi , Zhao Zhang , and Biao Li. Space-Curved Resonant Line Solitons in a Generalized $(2+1)$-Dimensional Fifth-Order KdV System[J]. Chin. Phys. Lett., 2021, 38(6): 090201
[8]	Wei Wang, Ruoxia Yao, and Senyue Lou. Abundant Traveling Wave Structures of (1+1)-Dimensional Sawada–Kotera Equation: Few Cycle Solitons and Soliton Molecules[J]. Chin. Phys. Lett., 2020, 37(10): 090201
[9]	Li-Chen Zhao, Yan-Hong Qin, Wen-Long Wang, Zhan-Ying Yang. A Direct Derivation of the Dark Soliton Excitation Energy[J]. Chin. Phys. Lett., 2020, 37(5): 090201
[10]	Danda Zhang, Da-Jun Zhang, Sen-Yue Lou. Lax Pairs of Integrable Systems in Bidifferential Graded Algebras[J]. Chin. Phys. Lett., 2020, 37(4): 090201
[11]	Yu-Han Wu, Chong Liu, Zhan-Ying Yang, Wen-Li Yang. Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction[J]. Chin. Phys. Lett., 2020, 37(4): 090201
[12]	Bao Wang, Zhao Zhang, Biao Li. Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schr?dinger Equation[J]. Chin. Phys. Lett., 2020, 37(3): 090201
[13]	Zhao Zhang, Shu-Xin Yang, Biao Li. Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation[J]. Chin. Phys. Lett., 2019, 36(12): 090201
[14]	Zhou-Zheng Kang, Tie-Cheng Xia. Construction of Multi-soliton Solutions of the $N$-Coupled Hirota Equations in an Optical Fiber[J]. Chin. Phys. Lett., 2019, 36(11): 090201
[15]	Yong-Shuai Zhang, Jing-Song He. Bound-State Soliton Solutions of the Nonlinear Schr?dinger Equation and Their Asymmetric Decompositions[J]. Chin. Phys. Lett., 2019, 36(3): 090201

Viewed

Full text

Abstract