Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations

doi:10.1088/1674-1056/27/4/040505

中国物理B ›› 2018, Vol. 27 ›› Issue (4): 40505-040505.doi: 10.1088/1674-1056/27/4/040505

Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations

Zai-Dong Li(李再东), Cong-Zhe Huo(霍丛哲), Qiu-Yan Li(李秋艳), Peng-Bin He(贺鹏斌), Tian-Fu Xu(徐天赋)

1. Department of Applied Physics, Hebei University of Technology, Tianjin 300401, China;
2. Key Laboratory of Electronic Materials and Devices of Tianjin, School of Electronics and Information Engineering, Hebei University of Technology, Tianjin 300401, China;
3. School of Physics and Electronics, Hunan University, Changsha 410082, China;
4. Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University, Qinhuangdao 066004, China

收稿日期:2017-11-11 修回日期:2018-01-02 出版日期:2018-04-05 发布日期:2018-04-05
通讯作者: Zai-Dong Li E-mail:lizd@hebut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11304270 and 61774001), the Key Project of Scientific and Technological Research of Hebei Province, China (Grant No. ZD2015133), the Construction Project of Graduate Demonstration Course of Hebei Province, China (Grant No. 94/220079), and the Natural Science Foundation of Hunan Province, China (Grant No. 2017JJ2045).

Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations

Zai-Dong Li(李再东)^1,2, Cong-Zhe Huo(霍丛哲)¹, Qiu-Yan Li(李秋艳)¹, Peng-Bin He(贺鹏斌)³, Tian-Fu Xu(徐天赋)⁴

1. Department of Applied Physics, Hebei University of Technology, Tianjin 300401, China;
2. Key Laboratory of Electronic Materials and Devices of Tianjin, School of Electronics and Information Engineering, Hebei University of Technology, Tianjin 300401, China;
3. School of Physics and Electronics, Hunan University, Changsha 410082, China;
4. Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University, Qinhuangdao 066004, China

Received:2017-11-11 Revised:2018-01-02 Online:2018-04-05 Published:2018-04-05
Contact: Zai-Dong Li E-mail:lizd@hebut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11304270 and 61774001), the Key Project of Scientific and Technological Research of Hebei Province, China (Grant No. ZD2015133), the Construction Project of Graduate Demonstration Course of Hebei Province, China (Grant No. 94/220079), and the Natural Science Foundation of Hunan Province, China (Grant No. 2017JJ2045).

摘要/Abstract

摘要： By means of the modified Darboux transformation we obtain some types of rogue waves in two-coupled nonlinear Schrödinger equations. Our results show that the two components admits the symmetry and asymmetry rogue wave solutions, which arises from the joint action of self-phase, cross-phase modulation, and coherent coupling term. We also obtain the analytical transformation from the initial seed solution to unique rogue waves with the bountiful pair structure. In a special case, the asymmetry rogue wave can own the spatial and temporal symmetry gradually, which is controlled by one parameter. It is worth pointing out that the rogue wave of two components can share the temporal inversion symmetry.

关键词: rogue wave, temporal inversion symmetry

Abstract: By means of the modified Darboux transformation we obtain some types of rogue waves in two-coupled nonlinear Schrödinger equations. Our results show that the two components admits the symmetry and asymmetry rogue wave solutions, which arises from the joint action of self-phase, cross-phase modulation, and coherent coupling term. We also obtain the analytical transformation from the initial seed solution to unique rogue waves with the bountiful pair structure. In a special case, the asymmetry rogue wave can own the spatial and temporal symmetry gradually, which is controlled by one parameter. It is worth pointing out that the rogue wave of two components can share the temporal inversion symmetry.

Key words: rogue wave, temporal inversion symmetry

中图分类号: (Solitons)

05.45.Yv

42.65.Tg (Optical solitons; nonlinear guided waves)

李再东, 霍丛哲, 李秋艳, 贺鹏斌, 徐天赋. Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations[J]. 中国物理B, 2018, 27(4): 40505-040505.

Zai-Dong Li(李再东), Cong-Zhe Huo(霍丛哲), Qiu-Yan Li(李秋艳), Peng-Bin He(贺鹏斌), Tian-Fu Xu(徐天赋). Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations[J]. Chin. Phys. B, 2018, 27(4): 40505-040505.

参考文献 55

[1]	Kharif C and Pelinovsky E 2003 Eur. J. Mech. B 22 603
[2]	Kharif C, Pelinovsky E and Slunyaev A 2009(Berlin, Heidelberg:Springer) 91
[3]	Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054
[4]	Kibler B, Fatome J, Finot C, Millot G, Dias F, Genty G, Akhmediev N and Dudley J M 2010 Nat. Phys. 6 790
[5]	Ruderman M S 2010 Eur. Phys. J. Spec. Top. 185 57
[6]	Moslem W M, Shukla P K and Eliasson B 2011 Euro. Phys. Lett. 96 25002
[7]	Zeba I, Yahia M E, Shukla P K and Moslem W M 2012 Phys. Lett. A 376 2309
[8]	Bludov Y V, Konotop V V and Akhmediev N 2009 Phys. Rev. A 80 2962
[9]	Chabchoub A, Hoffmann N P and Akhmediev N 2011 Phys. Rev. Lett. 106 204502
[10]	Chabchoub A, Hoffmann N P and Akhmediev N 2012 Geophys. J. Res. 117 100
[11]	Chabchoub A, Hoffmann N, Onorato M and Akhmediev N 2012 Phys. Rev. X 2 4089
[12]	Zhao F, Li Z D, Li Q Y, Wen L, Fu G S and Liu W M 2012 Ann. Phys. 327 2085
[13]	Li Z D, Li Q Y, Xu T F and He P B 2016 Phys. Rev. E 94 042202
[14]	Li Z D, Li Q Y and Liu W M 2017 J. Phys.:Conf. Ser. 827 012002
[15]	Liu Y K and Li B 2017 Chin. Phys. Lett. 34 10202
[16]	Qian C, Liu Y B and He J S 2016 Chin. Phys. Lett. 33 110201
[17]	Voronovich V V, Shrira V I and Thomas G 2008 J. Fluid Mech. 604 263
[18]	Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675
[19]	Ankiewicz A, Soto-Crespo J M and Akhmediev N 2010 Phys. Rev. E 81 046602
[20]	Akhmediev N, Ankiewicz A and Sotocrespo J M 2009 Phys. Rev. E 80 026601
[21]	He J S, Zhang H R, Wang L H, Porsezian K and Fokas A S 2012 Phys. Rev. E 87 052914
[22]	Wang L H, He J S, Xu H, Wang J and Porsezian K 2017 Phys. Rev. E 95 042217
[23]	Wang L H, Yang C H, Wang J and He J S 2017 Phys. Lett. A 381 1714
[24]	Bandelow U and Akhmediev N 2012 Phys. Rev. E 86 026606
[25]	Chen S 2013 Phys. Rev. E 88 023202
[26]	Peregrine D H 1983 Anziam. Journal 25 16
[27]	Chabchoub A, Hoffmann N P and Akhmediev N 2011 Phys. Rev. Lett. 106 204502
[28]	Wang Y, Song L J, Li L and Malomed Boris A 2015 J. Opt. Soc. Am. B 32 2257
[29]	Wang Y, Song L J and Li L 2016 Appl. Opt. 55 7241
[30]	Liu B, Li L and Malomed B A 2017 Eur. Phys. D 71 140
[31]	Ankiewicz A, Akhmediev N and Soto-Crespo J M 2010 Phys. Rev. E 82 026602
[32]	He J S, Xu S W and Porsezian K 2012 J. Phys. Soc. Jpn. 81 4007
[33]	He J S, Xu S W and Porsezian K 2012 Phys. Rev. E 86 066603
[34]	Xu S W, Porsezian K, He J S and Cheng Y 2013 Phys. Rev. E 88 062925
[35]	Xu S W, Porsezian K, He J S and Cheng Y 2016 Romanian Reports in Physics 68 316
[36]	He J S, Xu S, Porsezian K, Cheng Y and Dinda P T 2016 Phys. Rev. E 93 062201
[37]	Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202
[38]	Baronio F, Degasperis A, Conforti M and Wabnitz S 2012 Phys. Rev. Lett. 109 044102
[39]	Bludov Y V, Konotop V V, Akhmediev N 2010 Eur. Phys. J. Special Topics 185 169
[40]	Zhao L C and Liu J 2012 J. Opt. Soc. Am. B 29 3119
[41]	Baronio F, Conforti M, Degasperis A, Lombardo S, Onorato M and Wabnitz S 2014 Phys. Rev. Lett. 113 034101
[42]	Zhang G Q, Yan Z Y and Wen X Y 2017 Proc. Math. Phys. Eng. Sci. 473 0243
[43]	Yang G Y, Li L and Jia S 2012 Phys. Rev. E 85 046608
[44]	Yang G Y, Wang Y, Qin Z Y, Malomed B A, Mihalache D and Li L 2014 Phys. Rev. E 90 062909
[45]	Mikhailovet A V, Shabat A B and Yamilov R I 1987 Russ. Math. Surveys. 42 3
[46]	Hietarinta J 1987 Phys. Rep. 147 87
[47]	Zhao L C, Ling L M, Yang Z Y and Liu J 2015 Commun. Nonlinear Sci. Numer. Simulat. 23 21
[48]	Ling L M, Feng B F and Zhu Z N 2018 Nonlinear Analysis:Real World Applications 40 185
[49]	Dysthe K B and Pecseli H L 1977 Plasma Physics 19 931
[50]	Chen Y Y, Wang Q and Shi J L 2004 Acta Phys. Sin. 53 1070
[51]	Sakuma T and Kawanami Y 1984 Phys. Rev. B 29 880
[52]	Malomed B A 1992 Phys Rev A 22 403
[53]	Nakkeeran K 2001 J. Mod. Opt. 48 1863
[54]	Ling L M and Zhao L C 2015 Phys. Rev. E 92 022924
[55]	Sun W R, Tian B, Jiang Y and Zhen H L 2015 Phys. Rev. E 91 023205

Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations

Symmetry and asymmetry rogue waves in two-component coupled nonlinear Schrödinger equations

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 55

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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). Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation[J]. 中国物理B, 2022, 31(6): 60201-060201.
[2]	Yu-Qiang Yuan(袁玉强), Xiao-Yu Wu(武晓昱), and Zhong Du(杜仲). Rogue waves of a (3+1)-dimensional BKP equation[J]. 中国物理B, 2022, 31(12): 120202-120202.
[3]	Jun-Cai Pu(蒲俊才), Jun Li(李军), and Yong Chen(陈勇). Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints[J]. 中国物理B, 2021, 30(6): 60202-060202.
[4]	Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients[J]. 中国物理B, 2021, 30(11): 110202-110202.
[5]	王海峰, 张玉峰. Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation[J]. 中国物理B, 2020, 29(4): 40501-040501.
[6]	杜仲, 田播, 屈启兴, 赵学慧. Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber[J]. 中国物理B, 2020, 29(3): 30202-030202.
[7]	Abdselam Silem, 张成, 张大军. Dynamics of three nonisospectral nonlinear Schrödinger equations[J]. 中国物理B, 2019, 28(2): 20202-020202.
[8]	李再东, 王洋洋, 贺鹏斌. Formation mechanism of asymmetric breather and rogue waves in pair-transition-coupled nonlinear Schrödinger equations[J]. 中国物理B, 2019, 28(1): 10504-010504.
[9]	郑攀峰, 贾曼. A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation[J]. 中国物理B, 2018, 27(12): 120201-120201.
[10]	M S Alam,M G Hafez,M R Talukder,M Hossain Ali. Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma[J]. 中国物理B, 2017, 26(9): 95203-095203.
[11]	徐涛, 陈勇, 林机. Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics[J]. 中国物理B, 2017, 26(12): 120201-120201.
[12]	宋彩芹, 肖冬梅, 朱佐农. Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation[J]. 中国物理B, 2017, 26(10): 100204-100204.
[13]	王鑫, 陈勇. Rogue-wave pair and dark-bright-rogue wave solutions of the coupled Hirota equations[J]. 中国物理B, 2014, 23(7): 70203-070203.
[14]	张解放, 金美贞, 何纪达, 楼吉辉, 戴朝卿. Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides[J]. 中国物理B, 2013, 22(5): 54208-054208.
[15]	李传忠, 贺劲松, K. Porsezian. On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics[J]. 中国物理B, 2013, 22(4): 44208-044208.