A Variable-Coefficient Manakov Model and Its Explicit Solutions through the Generalized Dressing Method

doi:10.1088/0256-307X/30/6/060201

Chin. Phys. Lett.

2013, Vol. 30

Issue (6): 060201 DOI: 10.1088/0256-307X/30/6/060201

GENERAL

A Variable-Coefficient Manakov Model and Its Explicit Solutions through the Generalized Dressing Method

SU Ting^1**, DAI Hui-Hui², GENG Xian-Guo³

¹Department of Mathematical and Physical Science, Henan Institute of Engineering, Zhengzhou 451191
²Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
³Department of Mathematics, Zhengzhou University, Zhengzhou 450052

Cite this article:

SU Ting, DAI Hui-Hui, GENG Xian-Guo 2013 Chin. Phys. Lett. 30 060201

Download: PDF(467KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

For waves in inhomogeneous media, variable-coefficient evolution equations can arise. It is known that the Manakov model can derive two models for propagation in uniform optical fibers. If the fiber is nonuniform, one would expect that the coefficients in the model are not constants. We present a variable-coefficient Manakov model and derive its Lax pair using the generalized dressing method. As an application of the generalized dressing method, soliton solutions of the variable-coefficient Manakov model are obtained.

Received: 21 March 2013 Published: 31 May 2013

PACS:	02.30.Ik	(Integrable systems)
	02.30.Rz	(Integral equations)
	04.60.Nc	(Lattice and discrete methods)
	05.45.Yv	(Solitons)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/30/6/060201 OR https://cpl.iphy.ac.cn/Y2013/V30/I6/060201

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	SU Ting
	DAI Hui-Hui
	GENG Xian-Guo

[1] Zakharov V E and Shabat A B 1974 Funt. Anal. Appl. 8 226
[2] Zakharov V E and Shabat A B 1979 Funt. Anal. Appl. 13 166
[3] Chowdhury A R and Basak S 1984 J. Phys. A 17 L863
[4] Dye J M and Parker A 2000 J. Math. Phys. 41 2889
[5] Parker A 2001 Inverse Probl. 17 885
[6] Dai H H and Jeffrey A 1989 Phys. Lett. A 139 369
[7] Jeffrey A and Dai H H 1990 Rendiconti. Di Math. Ser. VII 10 439
[8] Porsezian K, Shanmugha S P and Mahalingam A 1994 Phys. Rev. E 50 1543
[9] Buryak A V, Kivshar Y S and Parker D F 1996 Phys. Lett. A 215 57
[10] Agrawal G P 1989 Nonlinear Fiber Optics (London: Academic)
[11] Tasgal R S and Potasek M J 1992 J. Math. Phys. 33 1208
[12] SaSa N and Satsuma J 1991 J. Phys. Soc. Jpn. 60 409
[13] Manakov S V 1973 Zh. Eksp. Teor. Fiz. 65 505
[14] Radharkishnan R, Lakshmanan M and Hietarinta J 1997 Phys. Rev. E 56 2213
[15] Lakshmanan M, Kanna T and Radharishnan R 2000 Rep. Math. Phys. 46 143
[16] Tsuchida T 2004 Prog. Theor. Phys. 111 151
[17] Tian B and Gao Y T 2005 Phys. Lett. A 342 228
[18] Porsezian K and Sundaram P S 1995 Chaos Solitons Fractals 5 119
[19] Ibrahim R S and El-Kalaawy O H 2007 Chaos Solitons Fractals 31 1001
[20] Manganaro N and Parker D F 1993 J. Phys. A: Math. Gen. 26 4093

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): 060201
[2]	Wen-Xiu Ma. Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions[J]. Chin. Phys. Lett., 2022, 39(10): 060201
[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): 060201
[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): 060201
[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): 060201
[6]	Yusong Cao and Junpeng Cao. Exact Solution of a Non-Hermitian Generalized Rabi Model[J]. Chin. Phys. Lett., 2021, 38(8): 060201
[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): 060201
[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): 060201
[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): 060201
[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): 060201
[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): 060201
[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): 060201
[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): 060201
[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): 060201
[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): 060201

Viewed

Full text

Abstract