Localized waves in three-component coupled nonlinear Schrödinger equation

doi:10.1088/1674-1056/25/9/090201

中国物理B ›› 2016, Vol. 25 ›› Issue (9): 90201-090201.doi: 10.1088/1674-1056/25/9/090201

• GENERAL • 下一篇

Localized waves in three-component coupled nonlinear Schrödinger equation

Tao Xu(徐涛), Yong Chen(陈勇)

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

收稿日期:2016-04-01 修回日期:2016-05-11 出版日期:2016-09-05 发布日期:2016-09-05
通讯作者: Yong Chen E-mail:ychen@sei.ecnu.edu.cn
基金资助:
Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).

Localized waves in three-component coupled nonlinear Schrödinger equation

Tao Xu(徐涛), Yong Chen(陈勇)

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

Received:2016-04-01 Revised:2016-05-11 Online:2016-09-05 Published:2016-09-05
Contact: Yong Chen E-mail:ychen@sei.ecnu.edu.cn
Supported by:
Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).

摘要/Abstract

摘要： We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.

关键词: localized waves, three-component coupled nonlinear Schrödinger equation, generalized Darboux transformation

Abstract: We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.

Key words: localized waves, three-component coupled nonlinear Schrödinger equation, generalized Darboux transformation

中图分类号: (Integrable systems)

02.30.Ik

03.75.Nt (Other Bose-Einstein condensation phenomena) 31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)

徐涛, 陈勇. Localized waves in three-component coupled nonlinear Schrödinger equation[J]. 中国物理B, 2016, 25(9): 90201-090201.

Tao Xu(徐涛), Yong Chen(陈勇). Localized waves in three-component coupled nonlinear Schrödinger equation[J]. Chin. Phys. B, 2016, 25(9): 90201-090201.

参考文献 37

[1]	Ma Y C 1979 Stud. Appl. Math. 60 43
[2]	Akhmediev N and Korneev V I 1986 Theor. Math. Phys. 69 1089
[3]	Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675
[4]	Chabchoub A, Hoffmann N, Onorato M and Akhmediev N 2012 Phys. Rev. X 2 011015
[5]	Ankiewicz A, Kedziora D J and Akhmediev N 2011 Phys. Lett. A 375 2782
[6]	Yan Z Y 2010 Commun. Theor. Phys. 54 947
[7]	Ling L M and Zhao L C 2013 Phys. Rev. E 88 043201
[8]	Ling L M, Guo B L and Zhao L C 2014 Phys. Rev. E 89 041201(R)
[9]	Guo B L, Ling L M and Liu Q P 2012 Phys. Rev. E 85 026607
[10]	Chan H N, Chow K W, Kedziora D J, Roger H J G and Edwin D 2014 Phys. Rev. E 89 032914
[11]	Guo B L, Ling L M and Liu Q P 2013 Stud. Appl. Math. 130 317
[12]	Wang X, Yang B, Chen Y amd Yang Y Q 2014 Phys. Scr. 89 095210
[13]	Zhang C C, Li C Z and He J S 2015 Math. Meth. Appl. Sci. 38 2411
[14]	Bayindir C 2016 arXiv:1602.05339
[15]	Bandelow U and Akhmediev N 2012 Phys. Lett. A 376 1558
[16]	Yang B, Zhang W G, Zhang H Q and Pei S B 2013 Phys. Scr. 88 065004
[17]	Hua W, Liu X S and Liu S X 2016 Chin. Phys. B 25 050202
[18]	Chen J C, Chen Y, Feng B F and Zhu H M 2014 Chin. Phys. Lett. 31 110502
[19]	Hu X R and Chen Y 2015 Chin. Phys. B 24 030201
[20]	Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202
[21]	Baronio F, Degasperis A, Conforti M and Wabnitz S 2012 Phys. Rev. Lett. 109 044102
[22]	Wang X, Yang B, Chen Y and Yang Y Q 2014 Chin. Phys. Lett. 31 090201
[23]	Wang X and Chen Y 2014 Chin. Phys. B 23 070203
[24]	Wang X, Li Y Q and Chen Y 2014 Wave Motion 51 1149
[25]	Chen S H and Song L Y 2013 Phys. Rev. E 87 032910
[26]	Zhao L C and Liu J 2013 Phys. Rev. E 87 013201
[27]	Baronio F, Conforti M, Degasperis A and Lombardo S 2013 Phys. Rev. Lett. 111 114101
[28]	Gu C H, Hu H S and Zhou Z X 2005 Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry (New York: Springer)
[29]	Ling L M, Zhao L C and Guo B L 2015 Nonlinearity 28 3243
[30]	Vijayajayanthi M, Kanna T and Lakshmanan M 2008 Phys. Rev. A 77 013820
[31]	Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin Heidelberg: Springer)
[32]	Li B and Chen Y 2007 Chaos Soliton. Fract. 33 532
[33]	Kedzioraa D J, Ankiewicz A and Akhmediev N 2014 Eur. Phys. J-Spec. Top. 223 43
[34]	Ling L M, Zhao L C and Guo B L 2016 Commun. Nonlinear Sci. Numer. Simulat. 32 285
[35]	Wang X, Cao J L and Chen Y 2015 Phys. Scr. 90 105201
[36]	Wang L, Li X, Qi F H and Zhang L L 2015 Ann. Phys. 359 97
[37]	Zhao L C, Ling L M, Yang Z Y and Liu J 2015 Commun. Nonlinear Sci. Numer. Simulat. 23 21

Localized waves in three-component coupled nonlinear Schrödinger equation

Localized waves in three-component coupled nonlinear Schrödinger equation

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