Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Recent developments of extreme wave events in integrable resonant systems

Pan Chang-Chang Baronio Fabio Chen Shi-Hua

Citation:

Recent developments of extreme wave events in integrable resonant systems

Pan Chang-Chang, Baronio Fabio, Chen Shi-Hua
PDF
HTML
Get Citation
  • From a microscopic perspective, the single extreme rogue wave event can be thought of as the spatiotemporally localized rational solutions of the underlying integrable model. A typical example is the fundamental Peregrine rogue wave, who in general entails a three-fold peak amplitude, while making its peak position arbitrary on a finite continuous-wave background. This kind of bizarre wave structure agrees well with the fleeting nature of realistic rogue waves and has been confirmed experimentally, first in nonlinear fibers, then in water wave tanks and plasmas, and recently in an irregular oceanic sea state. In this review, with a brief overview of the current state of the art of the concepts, methods, and research trends related to rogue wave events, we mainly discuss the fundamental Peregrine rogue wave solutions as well as their recent progress, intended for three typical integrable models, namely, the long-wave short-wave resonant equation, the three-wave resonant interaction equation, and the nonlinear Schrödinger and Maxwell–Bloch equation. Basically, while the first two models can describe the resonant interaction among optical waves, the latter governs the interaction between the optical waves and the resonant medium. For each integrable model, we present explicitly its Lax pair, Darboux transformation formulas, and fundamental Peregrine rogue wave solutions, in a self-consistent way. We confirm by convincing examples that these fundamental rogue wave solutions exhibit universality and can be applied to the multi-component or the higher-order versions of the current integrable models. By means of numerical simulations, we demonstrate as well several novel rogue wave dynamics such as coexisting rogue waves, complementary rogue waves, and Peregrine solitons of self-induced transparency.
      Corresponding author: Chen Shi-Hua, cshua@seu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11474051, 11974075)
    [1]

    Kharif C, Pelinovsky E, Slunyaev A 2009 Rogue Waves in the Ocean (Berlin: Springer)

    [2]

    Dysthe K, Krogstad H E, Müller P 2008 Annu. Rev. Fluid Mech. 40 287Google Scholar

    [3]

    Akhmediev N, Pelinovsky E 2010 Eur. Phys. J. Spec. Top. 185 1Google Scholar

    [4]

    Lawton G 2001 New Scientist 170 28

    [5]

    Pisarchik A N, Jaimes-Reátegui R, Sevilla-Escoboza R, Huerta-Cuellar G, Taki M 2011 Phys. Rev. Lett. 107 274101Google Scholar

    [6]

    Onorato M, Resitori S, Baronio F (ed) 2016 Rogue and Shock Waves in Nonlinear Dispersive Media (Switzerland: Springer) pp179–203

    [7]

    Wabnitz S (ed) 2017 Nonlinear Guided Wave Optics: A Testbed for Extreme Waves (Bristol: IOP Publishing) Chapt. 11

    [8]

    Dudley J M, Dias F, Erkintalo M, Genty G 2014 Nat. Photonics 8 755Google Scholar

    [9]

    Onorato M, Residori S, Bortolozzo U, Montina A, Arecchi F T 2013 Phys. Rep. 528 47Google Scholar

    [10]

    Moslem W M 2011 Phys. Plasmas 18 032301Google Scholar

    [11]

    Alam M S, Hafez M G, Talukder M R, Ali M Hossain 2017 Chin. Phys. B 26 095203Google Scholar

    [12]

    Tsai Y Y, Tsai J Y, Lin I 2016 Nat. Phys. 12 573Google Scholar

    [13]

    Bludov Yu V, Konotop V V, Akhmediev N 2009 Phys. Rev. A 80 033610Google Scholar

    [14]

    Wen L, Li L, Li Z D, Song S W, Zhang X F, Liu W M 2011 Eur. Phys. J. D 64 473Google Scholar

    [15]

    张解放, 戴朝卿 2016 物理学报 65 050501Google Scholar

    Zhang J F, Dai C Q 2016 Acta Phys. Sin. 65 050501Google Scholar

    [16]

    Liu C, Yang Z Y, Zhao L C, Yang W L, Yue R H 2013 Chin. Phys. Lett. 30 040304Google Scholar

    [17]

    Yan Z Y 2010 Commun. Theor. Phys. 54 947Google Scholar

    [18]

    Chabchoub A, Hoffmann N P, Akhmediev N 2011 Phys. Rev. Lett. 106 204502Google Scholar

    [19]

    Akhmediev N, Ankiewicz A, Taki M 2009 Phys. Lett. A 373 675Google Scholar

    [20]

    Solli D R, Ropers C, Koonath P, Jalali B 2007 Nature 450 1054Google Scholar

    [21]

    Lecaplain C, Grelu Ph, Soto-Crespo J M, Akhmediev N 2012 Phys. Rev. Lett. 108 233901Google Scholar

    [22]

    Baronio F, Degasperis A, Conforti M, Wabnitz S 2012 Phys. Rev. Lett. 109 044102Google Scholar

    [23]

    Chen S, Baronio F, Soto-Crespo J M, Grelu Ph, Mihalache D 2017 J. Phys. A: Math. Theor. 50 463001Google Scholar

    [24]

    Qiu D, He J, Zhang Y, Porsezian K 2015 Proc. R. Soc. A 471 20150236Google Scholar

    [25]

    Peregrine D H 1983 J. Aust. Math. Soc. Ser. B: Appl. Math. 25 16Google Scholar

    [26]

    Shrira V I, Geogjaev V V 2010 J. Eng. Math. 67 11Google Scholar

    [27]

    Kibler B, Fatome J, Finot C, Millot G, Dias F, Genty G, Akhmediev N, Dudley J M 2010 Nat. Phys. 6 790Google Scholar

    [28]

    Bailung H, Sharma S K, Nakamura Y 2011 Phys. Rev. Lett. 107 255005Google Scholar

    [29]

    Chabchoub A 2016 Phys. Rev. Lett. 117 144103Google Scholar

    [30]

    Walczak P, Randoux S, Suret P 2015 Phys. Rev. Lett. 114 143903Google Scholar

    [31]

    Picozzi A, Garnier J, Hansson T, Suret P, Randoux S, Millot G, Christodoulides D N 2014 Phys. Rep. 542 1Google Scholar

    [32]

    Soto-Crespo J M, Devine N, Akhmediev N 2016 Phys. Rev. Lett. 116 103901Google Scholar

    [33]

    Baronio F 2017 Opt. Lett. 42 1756Google Scholar

    [34]

    Baronio F, Chen S, Mihalache D 2017 Opt. Lett. 42 3514Google Scholar

    [35]

    Ankiewicz A, Soto-Crespo J M, Chowdhury M A, Akhmediev N 2013 J. Opt. Soc. Am. B 30 87Google Scholar

    [36]

    Zhang J F, Jin M Z, He J D, Lou J H, Dai C Q 2013 Chin. Phys. B 22 054208Google Scholar

    [37]

    Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507Google Scholar

    [38]

    Chen S, Soto-Crespo J M, Grelu Ph 2014 Opt. Express 22 27632Google Scholar

    [39]

    Guo B L, Ling L M 2011 Chin. Phys. Lett. 28 110202Google Scholar

    [40]

    Baronio F, Conforti M, Degasperis A, Lombardo S 2013 Phys. Rev. Lett. 111 114101Google Scholar

    [41]

    Grelu Ph (ed) 2016 Nonlinear Optical Cavity Dynamics: from Microresonators to Fiber Lasers (Weinheim: Wiley-VCH) pp231–316

    [42]

    Grelu Ph, Akhmediev N 2012 Nat. Photonics 6 84Google Scholar

    [43]

    Chen S, Dudley J M 2009 Phys. Rev. Lett. 102 233903Google Scholar

    [44]

    Akhmediev N, Ankiewicz A 1997 Solitons: Nonlinear Pulses and Beams (London: Chapman and Hall)

    [45]

    Chen S, Liu Y, Mysyrowicz A 2010 Phys. Rev. A 81 061806Google Scholar

    [46]

    Guo B, Ling L, Liu Q P 2012 Phys. Rev. E 85 026607Google Scholar

    [47]

    He J S, Zhang H R, Wang L H, Porsezian K, Fokas A S 2013 Phys. Rev. E 87 052914Google Scholar

    [48]

    Wang D S, Zhang D J, Yang J 2010 J. Math. Phys. 51 023510Google Scholar

    [49]

    Wang D S, Wang X 2018 Nonlinear Anal. Real World Appl. 41 334Google Scholar

    [50]

    Chen S, Zhou Y, Baronio F, Mihalache D 2018 Rom. Rep. Phys. 70 102

    [51]

    Akhmediev N, Ankiewicz A, Soto-Crespo J M 2009 Phys. Rev. E 80 026601Google Scholar

    [52]

    Ankiewicz A, Soto-Crespo J M, Akhmediev N 2010 Phys. Rev. E 81 046602Google Scholar

    [53]

    Chen S 2013 Phys. Rev. E 88 023202Google Scholar

    [54]

    Soto-Crespo J M, Devine N, Hoffmann N P, Akhmediev N 2014 Phys. Rev. E 90 032902Google Scholar

    [55]

    Chan H N, Chow K W, Kedziora D J, Grimshaw R H J, Ding E 2014 Phys. Rev. E 89 032914Google Scholar

    [56]

    Zhang Y, Guo L, He J, Zhou Z 2015 Lett. Math. Phys. 105 853Google Scholar

    [57]

    He J, Xu S, Porsezian K 2012 J. Phys. Soc. Jpn. 81 124007Google Scholar

    [58]

    Chen S, Song L Y 2014 Phys. Lett. A 378 1228Google Scholar

    [59]

    Xu S, He J, Cheng Y, Porseizan K 2015 Math. Method Appl. Sci. 38 1106Google Scholar

    [60]

    He J, Wang L, Li L, Porsezian K, Erdélyi R 2014 Phys. Rev. E 89 062917Google Scholar

    [61]

    Chen S, Soto-Crespo J M, Baronio F, Grelu Ph, Mihalache D 2016 Opt. Express 24 15251Google Scholar

    [62]

    Zha Q 2013 Phys. Scr. 87 065401Google Scholar

    [63]

    Chen S, Baronio F, Soto-Crespo J M, Liu Y, Grelu Ph 2016 Phys. Rev. E 93 062202Google Scholar

    [64]

    Chen S, Zhou Y, Bu L, Baronio F, Soto-Crespo J M, Mihalache D 2019 Opt. Express 27 11370Google Scholar

    [65]

    Ankiewicz A, Kedziora D J, Chowdury A, Bandelow U, Akhmediev N 2016 Phys. Rev. E 93 012206Google Scholar

    [66]

    Zhang Y, Guo L, Chabchoub A, He J 2017 Rom. J. Phys. 62 102

    [67]

    Chen S, Mihalache D 2015 J. Phys. A: Math. Theor. 48 215202Google Scholar

    [68]

    Baronio F, Conforti M, Degasperis A, Lombardo S, Onorato M, Wabnitz S 2014 Phys. Rev. Lett. 113 034101Google Scholar

    [69]

    Li L, Malomed B A, Mihalache D, Liu W M 2006 Phys. Rew. E 73 066610Google Scholar

    [70]

    Chen S, Song L Y 2013 Phys. Rev. E 87 032910Google Scholar

    [71]

    Li Z D, Huo C Z, Li Q Y, He P B, Xu T F 2018 Chin. Phys. B 27 040505Google Scholar

    [72]

    Ye Y, Zhou Y, Chen S, Baronio F, Grelu Ph 2019 Proc. R. Soc. A 475 20180806Google Scholar

    [73]

    Ohta Y, Yang J 2012 Phys. Rev. E 86 036604Google Scholar

    [74]

    Ohta Y, Yang J 2013 J. Phys. A: Math. Theor. 46 105202Google Scholar

    [75]

    Randoux S, Suret P, El G 2016 Sci. Rep. 6 29238Google Scholar

    [76]

    Matveev V B, Salle M A 1991 Darboux Transformation and Solitons (Berlin: Springer)

    [77]

    Hirota R 1973 J. Math. Phys. 14 805Google Scholar

    [78]

    Zhang N, Xia T C, Hu B B 2017 Commun. Theor. Phys. 68 580Google Scholar

    [79]

    Kang Z Z, Xia T C, Ma W X 2019 Adv. Differ. Equ. NY 2019 188Google Scholar

    [80]

    Kang Z Z, Xia T C, Ma W X 2019 Proc. Rom. Acad. A 20 115

    [81]

    Baronio F, Wabnitz S, Kodama Y 2016 Phys. Rev. Lett. 116 173901Google Scholar

    [82]

    Baronio F, Chen S, Onorato M, Trillo S, Wabnitz S, Kodama Y 2016 Opt. Lett. 41 5571Google Scholar

    [83]

    Bokaeeyan M, Ankiewicz A, Akhmediev N 2019 Phys. Scr. 94 035203Google Scholar

    [84]

    Mihalache D 2017 Rom. Rep. Phys. 69 403

    [85]

    Malomed B A, Mihalache D 2019 Rom. J. Phys. 64 106

    [86]

    Frisquet B, Kibler B, Morin Ph, Baronio F, Conforti M, Millot G, Wabnitz S 2016 Sci. Rep. 6 20785Google Scholar

    [87]

    Baronio F, Frisquet B, Chen S. Millot G, Wabnitz S, Kibler B 2018 Phys. Rev. A 97 013852Google Scholar

    [88]

    Tikan A, Billet C, El G, Tovbis A, Bertola M, Sylvestre T, Gustave F, Randoux S, Genty G, Suret P, Dudley J M 2017 Phys. Rev. Lett. 119 033901Google Scholar

    [89]

    Liu W, Zhang Y, He J 2018 Rom. Rep. Phys. 70 106

    [90]

    Chen S, Ye Y, Soto-Crespo J M, Grelu Ph, Baronio F 2018 Phys. Rev. Lett. 121 104101Google Scholar

    [91]

    Kibler B, Chabchoub A, Gelash A, Akhmediev N, Zakharov V E 2015 Phys. Rev. X 5 041026Google Scholar

    [92]

    Chen S, Grelu Ph, Soto-Crespo J M 2014 Phys. Rev. E 89 011201Google Scholar

    [93]

    Chen S, Baronio F, Soto-Crespo J M, Grelu Ph, Conforti M, Wabnitz S 2015 Phys. Rev. A 92 033847Google Scholar

    [94]

    He J, Xu S, Porseizan K 2012 Phys. Rev. E 86 066603Google Scholar

    [95]

    Chen S, Ye Y, Baronio F, Liu Y, Cai, X M, Grelu Ph 2017 Opt. Express 25 29687Google Scholar

    [96]

    Wang X, Li Y, Huang F, Chen Y 2015 Commun. Nonlinear Sci. Numer. Simul. 20 434Google Scholar

    [97]

    Degasperis A, Wabnitz S, Aceves A B 2015 Phys. Lett. A 379 1067Google Scholar

    [98]

    Guo L, Wang L, Cheng Y, He J 2017 Commun. Nonlinear Sci. Numer. Simul. 52 11Google Scholar

    [99]

    Zakharov V E 1972 Sov. Phys. JETP 35 908

    [100]

    Benney D J 1977 Stud. Appl. Math. 56 81Google Scholar

    [101]

    Djordjevic V D, Redekopp L G 1977 J. Fluid Mech. 79 703Google Scholar

    [102]

    Chowdhury A, Tataronis J A 2008 Phys. Rev. Lett. 100 153905Google Scholar

    [103]

    Shats M, Punzmann H, Xia H 2010 Phys. Rev. Lett. 104 104503Google Scholar

    [104]

    Chow K W, Chan H N, Kedziora D J, Grimshaw R H J 2013 J. Phys. Soc. Jpn. 82 074001Google Scholar

    [105]

    Chan H N, Grimshaw R H J, Chow K W 2018 Phys. Rev. Fluids 3 124801Google Scholar

    [106]

    Wright III O C 2006 Stud. Appl. Math. 117 71

    [107]

    Chen S 2014 Phys. Lett. A 378 1095Google Scholar

    [108]

    Baronio F, Chen S, Grelu Ph, Wabnitz S, Conforti M 2015 Phys. Rev. A 91 033804Google Scholar

    [109]

    Chen S, Soto-Crespo J M, Grelu Ph 2014 Phys. Rev. E 90 033203Google Scholar

    [110]

    Kaup D J, Reiman A, Bers A 1979 Rev. Mod. Phys. 51 275Google Scholar

    [111]

    Ibragimov E, Struthers A 1996 Opt. Lett. 21 1582Google Scholar

    [112]

    Conforti M, Baronio F, Degasperis A, Wabnitz S 2007 Opt. Express 15 12246Google Scholar

    [113]

    Abdolvand A, Nazarkin A, Chugreev A V, Kaminski C F, Russell P St J 2009 Phys. Rev. Lett. 103 183902Google Scholar

    [114]

    Picholle E, Montes C, Leycuras C, Legrand O, Botineau J 1991 Phys. Rev. Lett. 66 1454Google Scholar

    [115]

    Taranenko Y N, Kazovsky L G 1992 IEEE Photonics Technol. Lett. 4 494Google Scholar

    [116]

    Baronio F, Conforti M, Degasperis A, Wabnitz S 2008 IEEE J. Quantum Electron. 44 542Google Scholar

    [117]

    Picozzi A, Haelterman M 2001 Phys. Rev. Lett. 86 2010Google Scholar

    [118]

    Malkin V M, Shvets G, Fisch N J 1999 Phys. Rev. Lett. 82 4448Google Scholar

    [119]

    Buryak A V, Di Trapani P, Skryabin D V, Trillo S 2002 Phys. Rep. 370 63Google Scholar

    [120]

    Baronio F, Conforti M, De Angelis C, Degasperis A, Andreana M, Couderc V, Barthélémy A 2010 Phys. Rev. Lett. 104 113902Google Scholar

    [121]

    Degasperis A, Lombardo S 2006 Physica D 214 157Google Scholar

    [122]

    Chen S, Cai X M, Grelu Ph, Soto-Crespo J M, Wabnitz S, Baronio F 2016 Opt. Express 24 5886Google Scholar

    [123]

    Russell P St J, Culverhouse D, Farahi F 1991 IEEE J. Quantum Electron. 27 836Google Scholar

    [124]

    Allen L, Eberly J H 1975 Optical Resonance and Two-Level Atoms (New York: Wiley)

    [125]

    Haus H A 1979 Rev. Mod. Phys. 51 331Google Scholar

    [126]

    McCall S L, Hahn E L 1967 Phys. Rev. Lett. 18 908Google Scholar

    [127]

    Nakazawa M, Yamada E, Kubota H 1991 Phys. Rev. A 44 5973Google Scholar

    [128]

    He J S, Cheng Y, Li Y S 2002 Commun. Theor. Phys. 38 493Google Scholar

    [129]

    Li C, He J, Porsezian K 2013 Phys. Rev. E 87 012913Google Scholar

    [130]

    Conforti M, Baronio F 2011 Eur. Phys. J. D 64 115Google Scholar

    [131]

    Wu C F, Grimshaw R H J, Chow K W, Chan H N 2015 Chaos 25 103113Google Scholar

    [132]

    Tsuchida T 2002 J. Phys. A: Math. Gen. 35 7827Google Scholar

  • 图 1  数值模拟验证初始白噪声微扰下的基阶RW解(5)式, (6)式和 (10)式的稳定性, 左列图对应$(m, n) =(-1.3514, ~0.7803)$, 中列图对应$(m, n) =(- 0.4287, ~0.6442)$. 右列图显示这两类RW结构在同一背景场中的数值激发. 图改编自文献[109]

    Figure 1.  Simulations confirm the stability of the fundamental RW solutions (5), (6), and (10) against initial white noise perturbations. Left column: $(m, n) =(-1.3514, ~0.7803)$; Middle column: $(m, n) =(- 0.4287, ~0.6442)$. The right column shows the numerical excitation of such two rogue wave families from the same background field. Figure adapted from Ref. [109].

    图 2  互补型基阶RW解(18)式的数值模拟结果. 左列图: 未微扰情形; 右列图: 白噪声微扰情形. 图摘自文献[122]

    Figure 2.  Simulation results of the complementary fundamental rogue wave solutions (18). Left column: unperturbed; Right column: perturbed by initial white noises. Figure adapted from Ref. [122].

    图 3  NLS–MB方程的基阶RW解(23)的时空演化, 其中(a)列图对应解析解的3D曲面和轮廓图; (b)列图为数值模拟结果, 初始条件已文中给出; (c)列图显示这类异常波结构在背景场中的数值激发产生, 已黑线圈出. 图改编自文献[95]

    Figure 3.  Spatiotemporal evolution of the fundamental rogue wave solutions (23) of the NLS–MB equation. Column (a): Analytical solutions, given by 3D surface and contour plots; Column (b) the numerical results, with initial conditions being specified in the text; The column (c) shows the numerical excitation of the rogue waves, indicated by the black circles, from the background field. Figure adapted from Ref. [95].

  • [1]

    Kharif C, Pelinovsky E, Slunyaev A 2009 Rogue Waves in the Ocean (Berlin: Springer)

    [2]

    Dysthe K, Krogstad H E, Müller P 2008 Annu. Rev. Fluid Mech. 40 287Google Scholar

    [3]

    Akhmediev N, Pelinovsky E 2010 Eur. Phys. J. Spec. Top. 185 1Google Scholar

    [4]

    Lawton G 2001 New Scientist 170 28

    [5]

    Pisarchik A N, Jaimes-Reátegui R, Sevilla-Escoboza R, Huerta-Cuellar G, Taki M 2011 Phys. Rev. Lett. 107 274101Google Scholar

    [6]

    Onorato M, Resitori S, Baronio F (ed) 2016 Rogue and Shock Waves in Nonlinear Dispersive Media (Switzerland: Springer) pp179–203

    [7]

    Wabnitz S (ed) 2017 Nonlinear Guided Wave Optics: A Testbed for Extreme Waves (Bristol: IOP Publishing) Chapt. 11

    [8]

    Dudley J M, Dias F, Erkintalo M, Genty G 2014 Nat. Photonics 8 755Google Scholar

    [9]

    Onorato M, Residori S, Bortolozzo U, Montina A, Arecchi F T 2013 Phys. Rep. 528 47Google Scholar

    [10]

    Moslem W M 2011 Phys. Plasmas 18 032301Google Scholar

    [11]

    Alam M S, Hafez M G, Talukder M R, Ali M Hossain 2017 Chin. Phys. B 26 095203Google Scholar

    [12]

    Tsai Y Y, Tsai J Y, Lin I 2016 Nat. Phys. 12 573Google Scholar

    [13]

    Bludov Yu V, Konotop V V, Akhmediev N 2009 Phys. Rev. A 80 033610Google Scholar

    [14]

    Wen L, Li L, Li Z D, Song S W, Zhang X F, Liu W M 2011 Eur. Phys. J. D 64 473Google Scholar

    [15]

    张解放, 戴朝卿 2016 物理学报 65 050501Google Scholar

    Zhang J F, Dai C Q 2016 Acta Phys. Sin. 65 050501Google Scholar

    [16]

    Liu C, Yang Z Y, Zhao L C, Yang W L, Yue R H 2013 Chin. Phys. Lett. 30 040304Google Scholar

    [17]

    Yan Z Y 2010 Commun. Theor. Phys. 54 947Google Scholar

    [18]

    Chabchoub A, Hoffmann N P, Akhmediev N 2011 Phys. Rev. Lett. 106 204502Google Scholar

    [19]

    Akhmediev N, Ankiewicz A, Taki M 2009 Phys. Lett. A 373 675Google Scholar

    [20]

    Solli D R, Ropers C, Koonath P, Jalali B 2007 Nature 450 1054Google Scholar

    [21]

    Lecaplain C, Grelu Ph, Soto-Crespo J M, Akhmediev N 2012 Phys. Rev. Lett. 108 233901Google Scholar

    [22]

    Baronio F, Degasperis A, Conforti M, Wabnitz S 2012 Phys. Rev. Lett. 109 044102Google Scholar

    [23]

    Chen S, Baronio F, Soto-Crespo J M, Grelu Ph, Mihalache D 2017 J. Phys. A: Math. Theor. 50 463001Google Scholar

    [24]

    Qiu D, He J, Zhang Y, Porsezian K 2015 Proc. R. Soc. A 471 20150236Google Scholar

    [25]

    Peregrine D H 1983 J. Aust. Math. Soc. Ser. B: Appl. Math. 25 16Google Scholar

    [26]

    Shrira V I, Geogjaev V V 2010 J. Eng. Math. 67 11Google Scholar

    [27]

    Kibler B, Fatome J, Finot C, Millot G, Dias F, Genty G, Akhmediev N, Dudley J M 2010 Nat. Phys. 6 790Google Scholar

    [28]

    Bailung H, Sharma S K, Nakamura Y 2011 Phys. Rev. Lett. 107 255005Google Scholar

    [29]

    Chabchoub A 2016 Phys. Rev. Lett. 117 144103Google Scholar

    [30]

    Walczak P, Randoux S, Suret P 2015 Phys. Rev. Lett. 114 143903Google Scholar

    [31]

    Picozzi A, Garnier J, Hansson T, Suret P, Randoux S, Millot G, Christodoulides D N 2014 Phys. Rep. 542 1Google Scholar

    [32]

    Soto-Crespo J M, Devine N, Akhmediev N 2016 Phys. Rev. Lett. 116 103901Google Scholar

    [33]

    Baronio F 2017 Opt. Lett. 42 1756Google Scholar

    [34]

    Baronio F, Chen S, Mihalache D 2017 Opt. Lett. 42 3514Google Scholar

    [35]

    Ankiewicz A, Soto-Crespo J M, Chowdhury M A, Akhmediev N 2013 J. Opt. Soc. Am. B 30 87Google Scholar

    [36]

    Zhang J F, Jin M Z, He J D, Lou J H, Dai C Q 2013 Chin. Phys. B 22 054208Google Scholar

    [37]

    Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507Google Scholar

    [38]

    Chen S, Soto-Crespo J M, Grelu Ph 2014 Opt. Express 22 27632Google Scholar

    [39]

    Guo B L, Ling L M 2011 Chin. Phys. Lett. 28 110202Google Scholar

    [40]

    Baronio F, Conforti M, Degasperis A, Lombardo S 2013 Phys. Rev. Lett. 111 114101Google Scholar

    [41]

    Grelu Ph (ed) 2016 Nonlinear Optical Cavity Dynamics: from Microresonators to Fiber Lasers (Weinheim: Wiley-VCH) pp231–316

    [42]

    Grelu Ph, Akhmediev N 2012 Nat. Photonics 6 84Google Scholar

    [43]

    Chen S, Dudley J M 2009 Phys. Rev. Lett. 102 233903Google Scholar

    [44]

    Akhmediev N, Ankiewicz A 1997 Solitons: Nonlinear Pulses and Beams (London: Chapman and Hall)

    [45]

    Chen S, Liu Y, Mysyrowicz A 2010 Phys. Rev. A 81 061806Google Scholar

    [46]

    Guo B, Ling L, Liu Q P 2012 Phys. Rev. E 85 026607Google Scholar

    [47]

    He J S, Zhang H R, Wang L H, Porsezian K, Fokas A S 2013 Phys. Rev. E 87 052914Google Scholar

    [48]

    Wang D S, Zhang D J, Yang J 2010 J. Math. Phys. 51 023510Google Scholar

    [49]

    Wang D S, Wang X 2018 Nonlinear Anal. Real World Appl. 41 334Google Scholar

    [50]

    Chen S, Zhou Y, Baronio F, Mihalache D 2018 Rom. Rep. Phys. 70 102

    [51]

    Akhmediev N, Ankiewicz A, Soto-Crespo J M 2009 Phys. Rev. E 80 026601Google Scholar

    [52]

    Ankiewicz A, Soto-Crespo J M, Akhmediev N 2010 Phys. Rev. E 81 046602Google Scholar

    [53]

    Chen S 2013 Phys. Rev. E 88 023202Google Scholar

    [54]

    Soto-Crespo J M, Devine N, Hoffmann N P, Akhmediev N 2014 Phys. Rev. E 90 032902Google Scholar

    [55]

    Chan H N, Chow K W, Kedziora D J, Grimshaw R H J, Ding E 2014 Phys. Rev. E 89 032914Google Scholar

    [56]

    Zhang Y, Guo L, He J, Zhou Z 2015 Lett. Math. Phys. 105 853Google Scholar

    [57]

    He J, Xu S, Porsezian K 2012 J. Phys. Soc. Jpn. 81 124007Google Scholar

    [58]

    Chen S, Song L Y 2014 Phys. Lett. A 378 1228Google Scholar

    [59]

    Xu S, He J, Cheng Y, Porseizan K 2015 Math. Method Appl. Sci. 38 1106Google Scholar

    [60]

    He J, Wang L, Li L, Porsezian K, Erdélyi R 2014 Phys. Rev. E 89 062917Google Scholar

    [61]

    Chen S, Soto-Crespo J M, Baronio F, Grelu Ph, Mihalache D 2016 Opt. Express 24 15251Google Scholar

    [62]

    Zha Q 2013 Phys. Scr. 87 065401Google Scholar

    [63]

    Chen S, Baronio F, Soto-Crespo J M, Liu Y, Grelu Ph 2016 Phys. Rev. E 93 062202Google Scholar

    [64]

    Chen S, Zhou Y, Bu L, Baronio F, Soto-Crespo J M, Mihalache D 2019 Opt. Express 27 11370Google Scholar

    [65]

    Ankiewicz A, Kedziora D J, Chowdury A, Bandelow U, Akhmediev N 2016 Phys. Rev. E 93 012206Google Scholar

    [66]

    Zhang Y, Guo L, Chabchoub A, He J 2017 Rom. J. Phys. 62 102

    [67]

    Chen S, Mihalache D 2015 J. Phys. A: Math. Theor. 48 215202Google Scholar

    [68]

    Baronio F, Conforti M, Degasperis A, Lombardo S, Onorato M, Wabnitz S 2014 Phys. Rev. Lett. 113 034101Google Scholar

    [69]

    Li L, Malomed B A, Mihalache D, Liu W M 2006 Phys. Rew. E 73 066610Google Scholar

    [70]

    Chen S, Song L Y 2013 Phys. Rev. E 87 032910Google Scholar

    [71]

    Li Z D, Huo C Z, Li Q Y, He P B, Xu T F 2018 Chin. Phys. B 27 040505Google Scholar

    [72]

    Ye Y, Zhou Y, Chen S, Baronio F, Grelu Ph 2019 Proc. R. Soc. A 475 20180806Google Scholar

    [73]

    Ohta Y, Yang J 2012 Phys. Rev. E 86 036604Google Scholar

    [74]

    Ohta Y, Yang J 2013 J. Phys. A: Math. Theor. 46 105202Google Scholar

    [75]

    Randoux S, Suret P, El G 2016 Sci. Rep. 6 29238Google Scholar

    [76]

    Matveev V B, Salle M A 1991 Darboux Transformation and Solitons (Berlin: Springer)

    [77]

    Hirota R 1973 J. Math. Phys. 14 805Google Scholar

    [78]

    Zhang N, Xia T C, Hu B B 2017 Commun. Theor. Phys. 68 580Google Scholar

    [79]

    Kang Z Z, Xia T C, Ma W X 2019 Adv. Differ. Equ. NY 2019 188Google Scholar

    [80]

    Kang Z Z, Xia T C, Ma W X 2019 Proc. Rom. Acad. A 20 115

    [81]

    Baronio F, Wabnitz S, Kodama Y 2016 Phys. Rev. Lett. 116 173901Google Scholar

    [82]

    Baronio F, Chen S, Onorato M, Trillo S, Wabnitz S, Kodama Y 2016 Opt. Lett. 41 5571Google Scholar

    [83]

    Bokaeeyan M, Ankiewicz A, Akhmediev N 2019 Phys. Scr. 94 035203Google Scholar

    [84]

    Mihalache D 2017 Rom. Rep. Phys. 69 403

    [85]

    Malomed B A, Mihalache D 2019 Rom. J. Phys. 64 106

    [86]

    Frisquet B, Kibler B, Morin Ph, Baronio F, Conforti M, Millot G, Wabnitz S 2016 Sci. Rep. 6 20785Google Scholar

    [87]

    Baronio F, Frisquet B, Chen S. Millot G, Wabnitz S, Kibler B 2018 Phys. Rev. A 97 013852Google Scholar

    [88]

    Tikan A, Billet C, El G, Tovbis A, Bertola M, Sylvestre T, Gustave F, Randoux S, Genty G, Suret P, Dudley J M 2017 Phys. Rev. Lett. 119 033901Google Scholar

    [89]

    Liu W, Zhang Y, He J 2018 Rom. Rep. Phys. 70 106

    [90]

    Chen S, Ye Y, Soto-Crespo J M, Grelu Ph, Baronio F 2018 Phys. Rev. Lett. 121 104101Google Scholar

    [91]

    Kibler B, Chabchoub A, Gelash A, Akhmediev N, Zakharov V E 2015 Phys. Rev. X 5 041026Google Scholar

    [92]

    Chen S, Grelu Ph, Soto-Crespo J M 2014 Phys. Rev. E 89 011201Google Scholar

    [93]

    Chen S, Baronio F, Soto-Crespo J M, Grelu Ph, Conforti M, Wabnitz S 2015 Phys. Rev. A 92 033847Google Scholar

    [94]

    He J, Xu S, Porseizan K 2012 Phys. Rev. E 86 066603Google Scholar

    [95]

    Chen S, Ye Y, Baronio F, Liu Y, Cai, X M, Grelu Ph 2017 Opt. Express 25 29687Google Scholar

    [96]

    Wang X, Li Y, Huang F, Chen Y 2015 Commun. Nonlinear Sci. Numer. Simul. 20 434Google Scholar

    [97]

    Degasperis A, Wabnitz S, Aceves A B 2015 Phys. Lett. A 379 1067Google Scholar

    [98]

    Guo L, Wang L, Cheng Y, He J 2017 Commun. Nonlinear Sci. Numer. Simul. 52 11Google Scholar

    [99]

    Zakharov V E 1972 Sov. Phys. JETP 35 908

    [100]

    Benney D J 1977 Stud. Appl. Math. 56 81Google Scholar

    [101]

    Djordjevic V D, Redekopp L G 1977 J. Fluid Mech. 79 703Google Scholar

    [102]

    Chowdhury A, Tataronis J A 2008 Phys. Rev. Lett. 100 153905Google Scholar

    [103]

    Shats M, Punzmann H, Xia H 2010 Phys. Rev. Lett. 104 104503Google Scholar

    [104]

    Chow K W, Chan H N, Kedziora D J, Grimshaw R H J 2013 J. Phys. Soc. Jpn. 82 074001Google Scholar

    [105]

    Chan H N, Grimshaw R H J, Chow K W 2018 Phys. Rev. Fluids 3 124801Google Scholar

    [106]

    Wright III O C 2006 Stud. Appl. Math. 117 71

    [107]

    Chen S 2014 Phys. Lett. A 378 1095Google Scholar

    [108]

    Baronio F, Chen S, Grelu Ph, Wabnitz S, Conforti M 2015 Phys. Rev. A 91 033804Google Scholar

    [109]

    Chen S, Soto-Crespo J M, Grelu Ph 2014 Phys. Rev. E 90 033203Google Scholar

    [110]

    Kaup D J, Reiman A, Bers A 1979 Rev. Mod. Phys. 51 275Google Scholar

    [111]

    Ibragimov E, Struthers A 1996 Opt. Lett. 21 1582Google Scholar

    [112]

    Conforti M, Baronio F, Degasperis A, Wabnitz S 2007 Opt. Express 15 12246Google Scholar

    [113]

    Abdolvand A, Nazarkin A, Chugreev A V, Kaminski C F, Russell P St J 2009 Phys. Rev. Lett. 103 183902Google Scholar

    [114]

    Picholle E, Montes C, Leycuras C, Legrand O, Botineau J 1991 Phys. Rev. Lett. 66 1454Google Scholar

    [115]

    Taranenko Y N, Kazovsky L G 1992 IEEE Photonics Technol. Lett. 4 494Google Scholar

    [116]

    Baronio F, Conforti M, Degasperis A, Wabnitz S 2008 IEEE J. Quantum Electron. 44 542Google Scholar

    [117]

    Picozzi A, Haelterman M 2001 Phys. Rev. Lett. 86 2010Google Scholar

    [118]

    Malkin V M, Shvets G, Fisch N J 1999 Phys. Rev. Lett. 82 4448Google Scholar

    [119]

    Buryak A V, Di Trapani P, Skryabin D V, Trillo S 2002 Phys. Rep. 370 63Google Scholar

    [120]

    Baronio F, Conforti M, De Angelis C, Degasperis A, Andreana M, Couderc V, Barthélémy A 2010 Phys. Rev. Lett. 104 113902Google Scholar

    [121]

    Degasperis A, Lombardo S 2006 Physica D 214 157Google Scholar

    [122]

    Chen S, Cai X M, Grelu Ph, Soto-Crespo J M, Wabnitz S, Baronio F 2016 Opt. Express 24 5886Google Scholar

    [123]

    Russell P St J, Culverhouse D, Farahi F 1991 IEEE J. Quantum Electron. 27 836Google Scholar

    [124]

    Allen L, Eberly J H 1975 Optical Resonance and Two-Level Atoms (New York: Wiley)

    [125]

    Haus H A 1979 Rev. Mod. Phys. 51 331Google Scholar

    [126]

    McCall S L, Hahn E L 1967 Phys. Rev. Lett. 18 908Google Scholar

    [127]

    Nakazawa M, Yamada E, Kubota H 1991 Phys. Rev. A 44 5973Google Scholar

    [128]

    He J S, Cheng Y, Li Y S 2002 Commun. Theor. Phys. 38 493Google Scholar

    [129]

    Li C, He J, Porsezian K 2013 Phys. Rev. E 87 012913Google Scholar

    [130]

    Conforti M, Baronio F 2011 Eur. Phys. J. D 64 115Google Scholar

    [131]

    Wu C F, Grimshaw R H J, Chow K W, Chan H N 2015 Chaos 25 103113Google Scholar

    [132]

    Tsuchida T 2002 J. Phys. A: Math. Gen. 35 7827Google Scholar

  • [1] An Xin-Lei, Qiao Shuai, Zhang Li. Dynamic response and control of neuros based on electromagnetic field theory. Acta Physica Sinica, 2021, 70(5): 050501. doi: 10.7498/aps.70.20201347
    [2] Lai Yu-Cheng, Chen Su-Qi, Mou Lan-Ya, Wang Zhao-Na. Nanoscale electromagnetic boundary conditions based on Maxwell’s equations. Acta Physica Sinica, 2021, 70(23): 230301. doi: 10.7498/aps.70.20211025
    [3] Li Shu. Photon spectrum and angle distribution for photon scattering with relativistic Maxwellian electrons. Acta Physica Sinica, 2019, 68(1): 015201. doi: 10.7498/aps.68.20181796
    [4] Zhu Yan-Qing, Zhang Dan-Wei, Zhu Shi-Liang. Simulating Dirac, Weyl and Maxwell equations with cold atoms in optical lattices. Acta Physica Sinica, 2019, 68(4): 046701. doi: 10.7498/aps.68.20181929
    [5] Li Shu. Monte Carlo method for computing relativistic photon-Maxwellian electron scattering cross sections. Acta Physica Sinica, 2018, 67(21): 215201. doi: 10.7498/aps.67.20180932
    [6] Hu Liang, Luo Mao-Kang. Traveling wave solutions of the cylindrical nonlinear Maxwell's equations. Acta Physica Sinica, 2017, 66(13): 130302. doi: 10.7498/aps.66.130302
    [7] Lin Fu-Zhong, Ma Song-Hua. New exact solutions and complex wave excitations for the (2+1)-dimensional dispersive long wave equation. Acta Physica Sinica, 2014, 63(4): 040508. doi: 10.7498/aps.63.040508
    [8] Li Xue-Liang, Shi Yan-Xiang. Theoretical study on charging equation of dust plasmas in double Maxwellian distribution. Acta Physica Sinica, 2014, 63(21): 215201. doi: 10.7498/aps.63.215201
    [9] Wen Wen, Li Hui-Jun, Chen Bing-Yan. Evolution of interference patterns of strongly interacting Fermi gases in a harmonic trap. Acta Physica Sinica, 2012, 61(22): 220306. doi: 10.7498/aps.61.220306
    [10] Wang Ya-Wei, Liu Ming-Li, Liu Ren-Jie, Lei Hai-Na, Tian Xiang-Long. Fabry-Perot resonance on extraordinary transmission through one-dimensional metallic gratings with sub-wavelength under transverse electric wave excitation. Acta Physica Sinica, 2011, 60(2): 024217. doi: 10.7498/aps.60.024217
    [11] Mandafu, Naranmandula. Propagation and interaction property of solitary waves in a solid layer with energy influx. Acta Physica Sinica, 2010, 59(1): 60-66. doi: 10.7498/aps.59.60
    [12] Wang Yuan-Yuan, Zhang Cai-Hong, Ma Jin-Long, Jin Biao-Bing, Xu Wei-Wei, Kang Lin, Chen Jian, Wu Pei-Heng. Extraordinary transmission of sub-wavelength apertures in terahertz region. Acta Physica Sinica, 2009, 58(10): 6884-6888. doi: 10.7498/aps.58.6884
    [13] Jia Fei, Xie Shuang-Yuan, Yang Ya-Ping. Interaction of an atom with a field with varying frequency without rotating-wave approximation. Acta Physica Sinica, 2006, 55(11): 5835-5841. doi: 10.7498/aps.55.5835
    [14] Gong Hua-Rong, Gong Yu-Bin, Wei Yan-Yu, Tang Chang-Jian, Xue Dong-Hai, Wang Wen-Xiang. Analysis of ion noise with beam-wave interaction in klystron by two dimensional particle simulation method. Acta Physica Sinica, 2006, 55(10): 5368-5374. doi: 10.7498/aps.55.5368
    [15] Taogetusang, Sirendaoreji. New type of exact solitary wave solutions for dispersive long-wave equation and Benjamin equation. Acta Physica Sinica, 2006, 55(7): 3246-3254. doi: 10.7498/aps.55.3246
    [16] Guo Guan-Ping, Zhang Jie-Fang. Jacobi elliptic function expansion method applied to long-short wave interaction equations. Acta Physica Sinica, 2003, 52(11): 2660-2663. doi: 10.7498/aps.52.2660
    [17] LIU SAN-QIU, GUO QIN, TAO XIANG-YANG, FU CHUAN-HONG. QUANTUM DYNAMICS OF A CASCADE THREE-LEVEL ATOM INTERACTING WITH COHERENT STATE IN THE COUNTER ROTATING WAVE APPROXIMATION. Acta Physica Sinica, 1998, 47(9): 1481-1488. doi: 10.7498/aps.47.1481
    [18] YU WEI, XU ZHI-ZHAN, MA JIN-XIU, CHEN RONG-QING. DEVELOPMENT OF THREE-WAVE INTERACTIONS IN A PLASMA BEAT-WAVE ACCELERATOR. Acta Physica Sinica, 1993, 42(3): 431-436. doi: 10.7498/aps.42.431
    [19] HE KAI-FEN. HOPF BIFURCATION FROM STEADY STATE OF DISSIPATIVE THREE-WAVE INTERACTION. Acta Physica Sinica, 1987, 36(11): 1451-1458. doi: 10.7498/aps.36.1451
    [20] QIN YUN-WEN. ON THE FORM FACTOR OF RADIATION SCATTERING IN A BI-MAXWELLIAN PLASMA. Acta Physica Sinica, 1984, 33(4): 561-563. doi: 10.7498/aps.33.561
Metrics
  • Abstract views:  7319
  • PDF Downloads:  174
  • Cited By: 0
Publishing process
  • Received Date:  19 August 2019
  • Accepted Date:  28 October 2019
  • Available Online:  05 December 2019
  • Published Online:  05 January 2020

/

返回文章
返回