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Chin. Phys. B, 2013, Vol. 22(5): 054208    DOI: 10.1088/1674-1056/22/5/054208

Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides

Zhang Jie-Fanga, Jin Mei-Zhena, He Ji-Dab, Lou Ji-Huib, Dai Chao-Qingc
a Zhejiang University of Media and Communications, Hangzhou 310018, China;
b Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China;
c School of Sciences, Zhejiang Agriculture and Forestry University, Lin'an 311300, China
Abstract  We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schrödinger equation with varying coefficients. And then the dynamics of the first- and the second-order optical rogues are investigated. Finally, the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed. By properly choosing the distributed coefficients, we demonstrate analytically that rogue waves can be restrained or even be annihilated, or emerge periodically and sustain forever. We also figure out the center-of-mass motion of the rogue waves.
Keywords:  rogue wave      (2+1)-dimensional nonlinear Schrödinger equation      inhomogeneous nonlinear waveguides  
Received:  26 June 2012      Revised:  08 October 2012      Published:  01 April 2013
PACS:  42.65.-k (Nonlinear optics)  
  05.45.Yv (Solitons)  
  42.65.Tg (Optical solitons; nonlinear guided waves)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072219 and 11005092).
Corresponding Authors:  Zhang Jie-Fang     E-mail:

Cite this article: 

Zhang Jie-Fang, Jin Mei-Zhen, He Ji-Da, Lou Ji-Hui, Dai Chao-Qing Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides 2013 Chin. Phys. B 22 054208

[1] Kharif C, Pelinovsky E and Slunyaev A 2009 Rogue Waves in the Ocean, Observation, Theories and Modeling (New York: Springer)
[2] Draper L 1965 Marine Observer 35 193
[3] Peregrine D H 1983 J. Austral. Math. Soc. Ser. B 25 16
[4] Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675
[5] Ankiewicz A, Devine N and Akhmediev N 2009 Phys. Lett. A 373 3997
[6] Ruban V, Kodama Y and Ruderman M 2010 Eur. Phys. J. Spec. Top. 18 5
[7] Osborne A R 2009 Nonlinear Ocean Waves (New York: Academic Press)
[8] Müller P, Garrett Ch and Osborne A 2005 Oceanography. 18 66
[9] Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054
[10] Solli D R, Ropers C and Jalali B 2008 Phys. Rev. Lett. 101 233902
[11] Dudley J M, Genty G, Dias F, Kibler B and Akhmediev N 2009 Opt. Express 17 21497
[12] Dudley J M, Finot C, Millot G, Garnier J, Genty G, Agafontsev D and Dias F 2010 Eur. Phys. J. Spec. Top. 185 125
[13] Jalali B, Solli D R, Goda K, Tsia K and Ropers C 2010 Eur. Phys. J. Spec. Top. 185 145
[14] Kibler B, Fatome J, Finot C, Millot G, Dias F, Genty G, Akhmediev N and Dudley J M 2010 Nature Phys. 6 1
[15] Majus D, Jukna V, Valiulis G, Faccio D and Dubietis1 A 2011 Phys. Rev. A 83 025802
[16] Zaviyalov A, Egorov O, Iliew R and Lederer F 2012 Phys. Rev. A 85 013828
[17] Moslem W M, Sabry R, El-Labany S K and Shukla1 P K 2011 Phys. Rev. E 84 066402
[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] Yang G, Li L and Jia S T 2012 Phys. Rev. E 85 046608
[20] Dalfovo F, Giorgini S, Pitaevskii L P and Stringari S 1999 Rev. Mod. Phys. 71 463
[21] Bludov Y V, Konotop V V and Akhmediev N 2009 Phys. Rev. A 80 033610
[22] Ruderman M S 2010 Eur. Phys. J. Spec. Top. 185 57
[23] Montina A, Bortolozzo U, Residori S and Arecchi F T 2009 Phys. Rev. Lett. 103 173901
[24] Vergeles S and Turitsyn S K 2011 Phys. Rev. A 83 061801
[25] Stenflo L and Marklund M 2010 J. Plasma Phys. 76 293
[26] Yan Z Y 2010 Commun. Theor. Phys. 54 947
[27] Yan Z Y, Konotop V V and Akhmediev N 2010 Phys. Rev. E 82 036610
[28] Yan Z Y 2011 Phys. Lett. A 375 4274
[29] Yan Z Y 2011 J. Math. Anal. Appl. 380 689
[30] Wang G Y, He J S and Li Y S 2011 Commun. Theor. Phys. 56 995
[31] Xu S W, He J S and Wang L H 2011 J. Phys. A: Math. Theor. 44 305203
[32] Wang X C, He J S and Li Y S 2011 Commun. Theor. Phys. 56 631
[33] Akhmediev N, Ankiewicz A, and Soto-Crespo J M 2009 Phys. Rev. E 80 026601
[34] Kivshar Y S and Agrawal G P 2003 Optical Solitons: From Fibers to Photonic Crystals (San Diego: Academic)
[35] Tian Q, Yang Q, Dai C Q and Zhang J F 2011 Opt. Commun. 284 2222
[36] Hao R Y, Li L, Li Z H, Yang R C and Zhou G S 2005 Opt. Commun. 245 383
[37] Zhang J F, Tian Q, Wang Y Y, Dai C Q and Wu L 2010 Phys. Rev. A 81 023832
[38] Wu L, Li L and Zhang J F 2008 Phys. Rev. A 78 013838
[39] Wu L, Zhang J F, Li L, Tian Q and Porsezian K 2008 Opt. Express 16 6352
[40] Dai C Q, Wang Y Y and Wang X G 2011 J. Phys. A: Math. Theor. 44 155203
[41] Dai C Q, Wang Y Y and Yan C J 2010 Opt. Commun. 283 1489
[42] Wu L, Li L,Zhang J F, Mihalache D, Malomed B A and Liu W M 2010 Phys. Rev. A 81 061805
[43] Dai C Q, Zhang J F and Zhu S Q 2010 Europhys. Lett. 92 24005
[44] Zhong W P, Xie R H, Bellić M, Petrović N, Chen G and Yi L 2008 Phys. Rev. A 78 023821
[45] Zhong W P and Belić M 2009 Phys. Rev. A 79 023804
[46] Akhediev N, Soto-Crespo J M and Ankiweicz A 2009 Phys. Lett. A 373 2137
[47] Ankiewicz A, Clarkson P A and Akhmediev N 2010 J. Phys. A: Math. Theor. 43 122002
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