Controllable rogue waves in the nonautonomous nonlinear system with a linear potential

Regular Article

Abstract

Based on the similarity transformation connected the nonautonomous nonlinear Schrödinger equation with the autonomous nonlinear Schrödinger equation, we firstly derive self-similar rogue wave solutions (rational solutions) for the nonautonomous nonlinear system with a linear potential. Then, we investigate the controllable behaviors of one-rogue wave, two-rogue wave and rogue wave triplets in a soliton control system. Our results demonstrate that the propagation behaviors of rogue waves, including postpone, sustainment, recurrence and annihilation, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z m and the parameter Z 0. Moreover, the excitation time of controllable rogue waves is decided by the parameter T 0.

Keywords

Nonlinear Dynamics 

References

  1. 1.
    P.A.E.M. Janssen, J. Phys. Oceanogr. 33, 863 (2003)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373, 675 (2009)ADSMATHCrossRefGoogle Scholar
  3. 3.
    A. Ankiewicz, J.M. Soto-Crespo, N. Akhmediev, Phys. Rev. E 81, 046602 (2010)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Phys. Rev. A 80, 043818 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    A. Chabchoub, N.P. Hoffmann, N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    M. Shatz, H. Punzmann, H. Xia, Phys. Rev. Lett. 104, 104503 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    D.H. Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    N. Akhmediev, A. Ankiewicz, Phys. Rev. E 83, 046603 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    C. Kharif, E. Pelinovsky, A. Slyunyaev, Rogue waves in the ocean (Springer, Berlin, 2009)Google Scholar
  11. 11.
    J.M. Soto-Crespo, P. Grelu, N. Akhmediev, Phys. Rev. E 84, 016604 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    W.M. Moslem, P.K. Shukla, B. Eliasson, Europhys. Lett. 96, 25002 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    L. Wen, L. Li. Z.D. Li, X.F. Zhang, W.M. Liu, Eur. Phys. J. D 64, 473 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Z.Y. Yan, Phys. Lett. A 375, 4274 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    V.N. Serkin, A. Hasegawa, IEEE J. Sel. Top. Quant. Electron. 8, 418 (2002)CrossRefGoogle Scholar
  16. 16.
    C.Q. Dai, Y.Y. Wang, Q. Tian, J.F. Zhang, Ann. Phys. 327, 512 (2012)ADSMATHCrossRefGoogle Scholar
  17. 17.
    C.Q. Dai, Y.J. Xu, R.P. Chen, J.F. Zhang, Eur. Phys. J. D 59, 457 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    L.H. Zhao, C.Q. Dai, Eur. Phys. J. D 58, 327 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    X.J. Lai, X.O. Cai, Z. Naturforsch. A 66, 392 (2011)CrossRefGoogle Scholar
  20. 20.
    D.S. Wang, Y. Liu, Z. Naturforsch. A 65, 71 (2010)Google Scholar
  21. 21.
    D.S. Wang, X.H. Hu, J.P. Hu, W.M. Liu, Phys. Rev. A 81, 025604 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    W.J. Liu, B. Tian, T. Xu, K. Sun, Y. Jiang, Ann. Phys. 325, 1633 (2010)ADSMATHCrossRefGoogle Scholar
  23. 23.
    C.Q. Dai, R.P. Chen, J.F. Zhang, Chaos Solitons Fractals 44, 862 (2011)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    X.J. Lai, Commun. Theor. Phys. 55, 555 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    Y.X. Chen, X.H. Lu, Commun. Theor. Phys. 55, 871 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    A. Ankiewicz, D.J. Kedziora, N. Akhmediev, Phys. Lett. A 375, 2782 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Z.Y. Yan, Phys. Lett. A 374, 672 (2010)ADSMATHCrossRefGoogle Scholar
  28. 28.
    J.M. Dudley, C. Finot, D.J. Richardson, G. Millot, Nat. Phys. 3, 597 (2007)CrossRefGoogle Scholar
  29. 29.
    C.Q. Dai, Y.Y. Wang, J.F. Zhang, Opt. Lett. 35, 1437 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    C.Q. Dai, Q. Yang, J.D. He, Y.Y. Wang, Eur. Phys. J. D 63, 141 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Eur. Phys. J. Spec. Top. 185, 259 (2010)CrossRefGoogle Scholar
  32. 32.
    A. Hasegawa, M. Matsumoto, Optical Solitons in Fibers (Springer-Verlag, Berlin, 2003)Google Scholar
  33. 33.
    V.N. Serkina, A. Hasegawab, T.L. Belyaev, J. Mod. Opt. 57, 1456 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Z.Y. Sun, Y.T. Gao, X. Yu, Y. Liu, Europhys. Lett. 93, 40004 (2011)ADSCrossRefGoogle Scholar
  35. 35.
    Y.X. Chen, X.H. Lu, Phys. Scr. 85, 025010 (2012)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Ohta, J.K. Yang, Proc. R. Soc. A (2012), doi: 10.1098/rspa.2011.0640 (in press)Google Scholar
  37. 37.
    N. Akhmediev, V.M. Eleonskii, N.E. Kulagin, Sov. Phys. JETP 62, 894 (1985)Google Scholar
  38. 38.
    B.L. Lawrence, G.I. Stegeman, Opt. Lett. 23, 591 (1998)ADSCrossRefGoogle Scholar
  39. 39.
    S.L. Palacios, J.M. Fernández-Díaz, Opt. Commun. 178, 457 (2000)ADSCrossRefGoogle Scholar
  40. 40.
    L.L. Wang, C. Qian, C.Q. Dai, J.F. Zhang, Opt. Commun. 283, 4372 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of SciencesZhejiang A&F UniversityLin’an, ZhejiangP.R. China
  2. 2.School of Physical Science and TechnologySuzhou UniversitySuzhou, JiangsuP.R. China
  3. 3.College of Physics and Electromechanical EngineeringShaoguan UniversityGuangdongP.R. China
  4. 4.School of ScienceZhejiang Lishui UniversityLishui, ZhejiangP.R. China

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