Super rogue waves in coupled electric transmission lines


Coupled electric transmission lines (CETLs), which consist of a great number of identical sections, have been studied theoretically in the present paper. The super rogue wave (SRW) in CETLs is analyzed using the nonlinear Schrödinger equation. The dependence of the characteristics of the SRW parameters on CETLs is displayed in this paper. The results may be useful for exploiting or avoiding SRWs in CETLs.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. [1]

    F Yu, K G Lyon and E C Kan IEEE Microw. Wirel. Compon. Lett.22 618 (2012)

    Google Scholar 

  2. [2]

    J W Bragg, W W Sullivan, D Mauch, A A Neuber and J Dickens Rev. Sci. Instrum.84 054703 (2013)

    ADS  Google Scholar 

  3. [3]

    M J Rodwell, M Kamegawa, R Yu, M Case, E Carman and K S Giboney IEEE Trans. Microw. Theory Tech.39 1194 (1991)

    ADS  Google Scholar 

  4. [4]

    M Tan, C Su and W Anklam Electron. Lett.24 213 (1988)

    Google Scholar 

  5. [5]

    W X Li, Z W Guo, Z B Guo and Z H Qiang Commun. Theor. Phys.58 531 (2012)

    ADS  Google Scholar 

  6. [6]

    P L Christiansen, M P Sorensen and A C Scott Nonlinear Science at the Dawn of the 21st Century (Berlin: Springer) (2000)

    Google Scholar 

  7. [7]

    S B Leble Nonlinear Waves in Optical Waveguides and Soliton Theory Applications (Berlin: Springer) (2002)

    Google Scholar 

  8. [8]

    A I Dyachenko and V E Zakharov J. Exp. Theor. Phys. Lett.81 255 (2005)

    Google Scholar 

  9. [9]

    F Francesco, B Joseph, P D L Sonia, D John and D Frederic Sci. Rep.6 27715 (2016)

    ADS  Google Scholar 

  10. [10]

    V E Zakharov and L A Ostrovsky Phys. D Nonlinear Phenom.238 540 (2017)

    ADS  Google Scholar 

  11. [11]

    W P Su, J R Schrieffer and A J Heeger Phys. Rev. B22 2099 (1980)

    ADS  Google Scholar 

  12. [12]

    A D Boardman and K Xie Radio Sci.28 891 (2016)

    ADS  Google Scholar 

  13. [13]

    N N Akhmediev and A Ankiewicz Solitons: Nonlinear Pulses and Beams (Boca Raton: Chapman Hall) (1997)

    Google Scholar 

  14. [14]

    A Scott SIAM Rev.43 223 (2001)

    MathSciNet  Google Scholar 

  15. [15]

    Q Wang, X Li, J Zhang and Y Li Optik164 721 (2018)

    ADS  Google Scholar 

  16. [16]

    V Zakharov and A Gelash Nonlinear Sci. Exactly Solvable Integrable Syst.1109 620 (2012)

    Google Scholar 

  17. [17]

    M J Lighthill J. Appl. Math.1 1 (1965)

    Google Scholar 

  18. [18]

    B G Whitham J. Fluid Mech.22 273 (1965)

    ADS  MathSciNet  Google Scholar 

  19. [19]

    S F Tian J. Differ. Equ.262 506 (2017)

    ADS  Google Scholar 

  20. [20]

    S F Tian Proc. R. Soc. A472 0588 (2016)

    Google Scholar 

  21. [21]

    L L Feng and T T Zhang Appl. Math. Lett.78 133 (2018)

    MathSciNet  Google Scholar 

  22. [22]

    Z Du, B Tian, H P Chai, Y Sun and X H Zhao Chaos Solitons Fractals109 90 (2018)

    ADS  MathSciNet  Google Scholar 

  23. [23]

    C R Zhang, B Tian, X Y Wu, Y Q Yuan and X X Du Phys. Scr.93 095202 (2018)

    ADS  Google Scholar 

  24. [24]

    W Q Peng, S F Tian, T T Zhang Europhys. Lett.123 50005 (2018)

    ADS  Google Scholar 

  25. [25]

    X B Wang, T T Zhang, M J Dong Appl. Math. Lett.86 298 (2018)

    MathSciNet  Google Scholar 

  26. [26]

    X B Wang, S F Tian, C Y Qin and T T Zhang Appl. Math. Lett.68 40 (2017)

    MathSciNet  Google Scholar 

  27. [27]

    C Y Qin, S F Tian, X B Wang, T T Zhang and J Li Comput. Math. Appl.75 4221 (2018)

    MathSciNet  Google Scholar 

  28. [28]

    X W Yan, S F Tian, M J Dong, L Zhou and T T Zhang Comput. Math. Appl.76 179 (2018)

    MathSciNet  Google Scholar 

  29. [29]

    X Y Gao Appl. Math. Lett.73 143 (2017)

    MathSciNet  Google Scholar 

  30. [30]

    M J Dong, S F Tian, X W Yan and L Zou Comput. Math. Appl.75 957 (2018)

    MathSciNet  Google Scholar 

  31. [31]

    L Liu, B Tian, Y Q Yuan and Z Du Phys. Rev. E97 052217 (2018)

    ADS  MathSciNet  Google Scholar 

  32. [32]

    X Y Wu, B Tian, L Liu and Y Sun Comput. Math. Appl.76 215 (2018)

    MathSciNet  Google Scholar 

  33. [33]

    C C Hu, B Tian, X Y Wu, Y Q Yuan and Z Du Eur. Phys. J. Plus133 40 (2018)

    Google Scholar 

  34. [34]

    X H Zhao, B Tian, X Y Xie, X Y Wu, Y Sun and Y J Guo Waves Random Complex Media28 356 (2018)

    ADS  MathSciNet  Google Scholar 

  35. [35]

    Y Q Yuan, B Tian, L Liu, X Y Wu and Y Sun J. Math. Anal. Appl.460 476 (2018)

    MathSciNet  Google Scholar 

  36. [36]

    X Y Gao Appl. Math. Lett.91 165 (2019)

    MathSciNet  Google Scholar 

  37. [37]

    V E Zakharov and A B Shabat J. Exp. Theor. Phys.37 823 (1973)

    ADS  Google Scholar 

  38. [38]

    N K Vitanov, A Chabchoub and N Hoffmann J. Theor. Appl. Mech.43 43 (2013)

    Google Scholar 

  39. [39]

    J He Rom. J. Phys.62 203 (2017)

    Google Scholar 

  40. [40]

    F Baronio, B Frisquet, S Chen, G Millot, S Wabnitz and B Kibler Phys. Rev. A97 13852 (2018)

    ADS  Google Scholar 

  41. [41]

    J M Dudley, F Dias, M Erkintalo and G Genty Nat. Photonics8 755 (2014)

    ADS  Google Scholar 

  42. [42]

    M Bacha, M Tribeche and P K Shukla Phys. Rev. E Stat. Nonlinear Soft Matter Phys.85 056413 (2012)

    ADS  Google Scholar 

  43. [43]

    M Emamuddin, M M Masud and A A Mamun Astrophys. Space Sci.349 821 (2014)

    ADS  Google Scholar 

  44. [44]

    J Tamang, K Sarkar and A Saha Phys. A Stat. Mech. Appl.505 18 (2018)

    Google Scholar 

  45. [45]

    V B Efimov, A N Ganshin, G V Kolmakov, P V E Mcclintock and L P Mezhov-Deglin Eur. Phys. J. Special Top.185 181 (2010)

    ADS  Google Scholar 

  46. [46]

    Y V Bludov and V V Konotop Phys. Rev. A81 15780 (2010)

    Google Scholar 

  47. [47]

    M Onorato, S Residori, U Bortolozzo, A Montina and F T Arecchi Phys. Rep.528 47 (2013)

    ADS  MathSciNet  Google Scholar 

  48. [48]

    P Marquie, J M Bilbault and M Remoissenet Phys. Rev. E49 828 (1994)

    ADS  Google Scholar 

  49. [49]

    Y Nejoh J. Phys. A Gen. Phys.20 1733 (1999)

    ADS  MathSciNet  Google Scholar 

  50. [50]

    F B Pelap and M M Faye Nonlinear Oscil.8 513 (2005)

    MathSciNet  Google Scholar 

  51. [51]

    W S Duan Europhys. Lett.66 192 (2004)

    ADS  Google Scholar 

  52. [52]

    T Yoshinaga and T Kakutani J. Phys. Soc. Jpn.56 3447 (1987)

    ADS  Google Scholar 

  53. [53]

    N Akhmediev, A Ankiewicz and M Taki Phys. Lett. A373 675 (2009)

    ADS  Google Scholar 

  54. [54]

    A Slunyaev, E Pelinovsky, A Sergeeva, A Chabchoub, N Hoffmann, M Onorato and N Akhmediev Phys. Rev. E88 012909 (2013)

    ADS  Google Scholar 

  55. [55]

    D Peregrine ANZIAM J.25 16 (1983)

    Google Scholar 

  56. [56]

    V I Shrira and V V Geogjaev J. Eng. Math.67 11 (2010)

    Google Scholar 

Download references


This research is funded by the NSFC (National Natural Science Foundation of China) project under Grant Number 41861047 and Northwest Normal University Young Teachers’ Research Capability Enhancement Team Project under Grant Number NWNU-LKQN-1706.

Author information



Corresponding author

Correspondence to Yu Long Bai.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Duan, J.K., Bai, Y.L., Wei, Q. et al. Super rogue waves in coupled electric transmission lines. Indian J Phys 94, 879–883 (2020).

Download citation


  • Nonlinear system
  • Super rogue wave
  • Transmission lines


  • 05.45.-a
  • 05.45.Yv
  • 84.70.+p