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Integrability and solitons for the higher-order nonlinear Schrödinger equation with space-dependent coefficients in an optical fiber

  • Jing-Jing Su
  • Yi-Tian Gao
Regular Article

Abstract.

Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.

References

  1. 1.
    A. Biswas, M. Mirzazadeh, M. Savescu, D. Milovic, K.R. Khan, M.F. Mahmood, M. Belic, J. Mod. Opt. 61, 1550 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    Q. Zhou, Q.P. Zhu, Y.X. Liu, H. Yu, P. Yao, A. Biswas, Laser Phys. 25, 015402 (2015)ADSCrossRefGoogle Scholar
  3. 3.
    A. Biswas, J. Opt. A 4, 84 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973)ADSCrossRefGoogle Scholar
  5. 5.
    Q. Zhou, Q.P. Zhu, L. Moraru, A. Biswas, Optoelectron. Adv. Mat. 16, 995 (2014)Google Scholar
  6. 6.
    A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973)ADSCrossRefGoogle Scholar
  7. 7.
    M. Savescu, A.H. Bhrawy, E.M. Hilal, A.A. Alshaery, A. Biswas, Rom. J. Phys. 59, 582 (2014)Google Scholar
  8. 8.
    A. Hasegawa, Optical Solitons in Fibers, in Springer Tracts in Modern Physics, (Springer, Berlin, 1992)Google Scholar
  9. 9.
    E.A. Kuznetsov, A.M. Rubenchik, V.E. Zakharov, Phys. Rep. 142, 103 (1986)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    B. Movaghar, I.A. Howard, Synth. Met. 27, A61 (1988)CrossRefGoogle Scholar
  11. 11.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    M.J. Ablowitz, G. Biondini, L.A. Ostrovsky, Chaos 10, 471 (2000)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Q. Zhou, Y. Zhong, M. Mirzazadeh, A.H. Bhrawy, E. Zerrad, A. Biswas, Wave Random Complex 26, 204 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    A. Biswas, A.J.M. Jawad, W.N. Manrakhan, A.K. Sarma, K.R. Khan, Opt. Laser Technol. 44, 2265 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    A. Biswas, A.H. Bhrawy, A.A. Alshaery, E.M. Hilal, Optik 125, 4946 (2014)ADSGoogle Scholar
  16. 16.
    J. Chai, B. Tian, H.L. Zhen, W.R. Sun, Ann. Phys. 359, 371 (2015)CrossRefGoogle Scholar
  17. 17.
    Q. Zhou, Q.P. Zhu, Y.X. Liu, H. Yu, C. Wei, P. Yao, A.H. Bhrawy, A. Biswas, Laser Phys. 25, 025402 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    A. Biswas, K.R. Khan, M.F. Mahmood, M. Belic, Optik 125, 3299 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    E. Bourkoff, W. Zhao, R.I. Joseph, D.N. Christodoulides, Opt. Lett. 12, 272 (1987)ADSCrossRefGoogle Scholar
  20. 20.
    I.P. Christov, Phys. Rev. A 60, 3244 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    F. DeMartini, Phys. Rev. 164, 312 (1967)ADSCrossRefGoogle Scholar
  22. 22.
    G. Yang, Y.R. Shen, Opt. Lett. 9, 510 (1984)ADSCrossRefGoogle Scholar
  23. 23.
    D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983)ADSCrossRefGoogle Scholar
  24. 24.
    R. Hirota, J. Math. Phys. 14, 805 (1973)ADSCrossRefGoogle Scholar
  25. 25.
    K. Porsezian, M. Daniel, M. Lakshmanan, J. Math. Phys. 33, 1807 (1992)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    M. Daniel, L. Kavitha, R. Amuda, Phys. Rev. B 59, 13774 (1999)ADSCrossRefGoogle Scholar
  27. 27.
    A. Ankiewicz, D.J. Kedziora, A. Chowdury, U. Bandelow, N. Akhmediev, Phys. Rev. E 93, 012206 (2016)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    V.I. Kruglov, A.C. Peacock, J.M. Dudley, J.D. Harvey, Opt. Lett. 25, 1753 (2000)ADSCrossRefGoogle Scholar
  29. 29.
    M. Eslami, M. Mirzazadeh, A. Biswas, J. Mod. Opt. 60, 1627 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    J.J. Su, Y.T. Gao, S.L. Jia, Commun. Nonlinear Sci. Numer. Simul. 50, 128 (2017)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    H. Triki, S. Crutcher, A. Yildirim, T. Hayat, O.M. Aldossary, A. Biswas, Rom. Rep. Phys. 64, 367 (2012)Google Scholar
  32. 32.
    A. Biswas, Y. Yildirim, E. Yasar, H. Triki, A.S. Alshomrani, M.Z. Ullah, Q. Zhou, S.P. Moshokoa, M. Belic, Optik 157, 1235 (2018)ADSCrossRefGoogle Scholar
  33. 33.
    A. Biswas, A.J.M. Jawad, Q. Zhou, Optik 157, 525 (2018)ADSCrossRefGoogle Scholar
  34. 34.
    M. Savescu, Q. Zhou, L. Moraru, A. Biswas, S.P. Moshokoa, M. Belic, Optik 127, 8995 (2016)ADSCrossRefGoogle Scholar
  35. 35.
    M. Savescu, A.H. Bhrawy, E.M. Hilal, A.A. Alshaery, L. Moraru, A. Biswas, Optoelectron. Adv. Mat. 9, 10 (2015)Google Scholar
  36. 36.
    J. Vega-Guzman, E.M. Hilal, A.A. Alshaery, A.H. Bhrawy, M.F. Mahmood, L. Moraru, A. Biswas, Proc. Rom. Acad. A 16, 41 (2015)Google Scholar
  37. 37.
    G. Ebadi, A. Mojavir, J. Vega-Guzman, K.R. Khan, M.F. Mahmood, L. Moraru, A. Biswas, M. Belic, J. Optoelectron. Adv. Mater. 8, 828 (2014)Google Scholar
  38. 38.
    J. Vega-Guzman, A.A. Alshaery, E.M. Hilal, A.H. Bhrawy, M.F. Mahmood, L. Moraru, A. Biswas, J. Optoelectron. Adv. Mater. 16, 1063 (2014)Google Scholar
  39. 39.
    A.A. Alshaery, E.M. Hilal, M.A. Banaja, S.A. Alkhateeb, L. Moraru, A. Biswas, J. Optoelectron. Adv. Mater. 16, 750 (2014)Google Scholar
  40. 40.
    B. Tian, W.R. Shan, C.Y. Zhang, G.M. Wei, Y.T. Gao, Eur. Phys. J. B 47, 329 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid DynamicsBeijing University of Aeronautics and AstronauticsBeijingChina

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