Solitons and breather-to-soliton transitions for an integrable higher-order variable-coefficient nonlinear Schrödinger equation in an optical fiber

  • Xiao-Yue Jia
  • Bo Tian
  • Lei Liu
  • Xiao-Yu Wu
  • Yan Sun
Regular Article
  • 28 Downloads

Abstract.

Under investigation in this paper is an integrable eighth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber. One-, two-, three-soliton and the first-, second-order breather solutions are obtained via the Darboux transformation. Properties of the solitons are discussed graphically. Breather-to-soliton transitions are studied under certain constraints. Discussions indicate that the soliton amplitude is not related to the variable coefficients, but related to some spectral parameters, while the soliton velocity is related to both the variable coefficients and spectral parameters. We find that there are two types of the breather-to-soliton transitions, M-shaped and W-shaped, which are determined through the spectral parameters.

References

  1. 1.
    L. Wang, Z.Q. Wang, W.R. Sun, Y.Y. Shi, M. Li, M. Xu, Commun. Nonlinear Sci. Numer. Simul. 47, 190 (2017)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Wang, Y.J. Zhu, F.H. Qi, M. Li, R. Guo, Chaos 25, 063111 (2015)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    L. Wang, J.H. Zhang, Z.Q. Wang, C. Liu, M. Li, F.H. Qi, R. Guo, Phys. Rev. E 93, 012214 (2016)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    L. Wang, X. Li, F.H. Qi, L.L. Zhang, Ann. Phys. 359, 97 (2015)CrossRefGoogle Scholar
  5. 5.
    B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, J.M. Dudley, Sci. Rep. 2, 463 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    J.M. Dudley, F. Dias, M. Erkintalo, G. Genty, Nat. Photon. 8, 755 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    L. Wang, J.H. Zhang, C. Liu, M. Li, F.H. Qi, Phys. Rev. E 93, 062217 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    Q.M. Huang, Y.T. Gao, L. Hu, Appl. Math. Lett. 75, 135 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    P. Jin, C.A. Bouman, K.D. Sauer, IEEE Trans. Comput. Imaging 1, 200 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    T.T. Jia, Y.Z. Chai, H.Q. Hao, Math. Probl. Eng. 2016, 1741245 (2016)Google Scholar
  11. 11.
    T.T. Jia, Y.Z. Chai, H.Q. Hao, Superlattice Microstruct. 105, 172 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    A. Maccari, Electron. J. Theor. Phys. 3, 39 (2006)Google Scholar
  13. 13.
    J.J. Su, Y.T. Gao, Superlattice Microstruct. 104, 498 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    J.J. Su, Y.T. Gao, Eur. Phys. J. Plus 132, 53 (2017)CrossRefGoogle Scholar
  15. 15.
    G.F. Deng, Y.T. Gao, Superlattice Microstruct. 109, 345 (2017)CrossRefGoogle Scholar
  16. 16.
    S. Beauno, M.M. Latha, Int. J. Adv. Res. Sci. Technol. 1, 93 (2015)Google Scholar
  17. 17.
    L. Wang, D.Y. Jiang, F.H. Qi, Y.Y. Shi, Y.C. Zhao, Commun. Nonlinear Sci. Numer. Simul. 42, 502 (2017)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    J.M. Dudley, J.R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University Press, Cambridge, 2010)Google Scholar
  19. 19.
    D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983)ADSCrossRefGoogle Scholar
  20. 20.
    J.J. Su, Y.T. Gao, S.L. Jia, Commun. Nonlinear Sci. Numer. Simul. 50, 128 (2017)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    M. Daniel, L. Kavitha, R. Amuda, Phys. Rev. B 59, 13774 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    J.H. Zhang, L. Wang, C. Liu, Proc. R. Soc. A 473, 20160681 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    X.Y. Gao, Appl. Math. Lett. 73, 143 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    A. Ankiewicz, D.J. Kedziora, A. Chowdury, U. Bandelow, N. Akhmediev, Phys. Rev. E 93, 012206 (2016)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    S.L. Jia, Y.T. Gao, C. Zhao, J.W. Yang, Y.J. Feng, Waves Random Complex Media 27, 544 (2017)CrossRefGoogle Scholar
  26. 26.
    A. Chowdury, D.J. Kedziora, A. Ankiewicz, N. Akhmediev, Phys. Rev. E 91, 032928 (2015)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    A. Chowdury, A. Ankiewicz, N. Akhmediev, Proc. R. Soc. A 471, 20150130 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    Q.M. Huang, Y.T. Gao, S.L. Jia, Y.L. Wang, G.F. Deng, Nonlinear Dyn. 87, 2529 (2017)CrossRefGoogle Scholar
  29. 29.
    Q.M. Huang, Y.T. Gao, Nonlinear Dyn. 89, 2855 (2017)CrossRefGoogle Scholar
  30. 30.
    X.Y. Gao, Ocean Eng. 96, 245 (2015)CrossRefGoogle Scholar
  31. 31.
    D.J. Kedziora, A. Ankiewicz, A. Chowdury, N. Akhmediev, Chaos 25, 103114 (2015)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur, Phys. Rev. Lett. 31, 125 (1973)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Y. Tao, J. He, Phys. Rev. E 85, 026601 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    W.R. Sun, Ann. Phys. (Berlin) 529, 1600227 (2017)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Xiao-Yue Jia
    • 1
  • Bo Tian
    • 1
  • Lei Liu
    • 1
  • Xiao-Yu Wu
    • 1
  • Yan Sun
    • 1
  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina

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