Skip to main content
SpringerLink
Log in

Nonlinear localized wave conversions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system with quintic terms in an erbium-doped fiber

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We discuss the possibility of breather-to-soliton conversions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system with quintic terms describing the propagation of ultrashort optical pulses, up to the attosecond duration, in an erbium-doped fiber. The analytic forms for the vector breather solutions of that system with complex (not pure imaginary) eigenvalues are obtained with the Darboux transformation. With the special values of the eigenvalues, we find that vector breather solutions can be converted into the vector soliton solutions on the constant (not zero) backgrounds. The condition for such conversion is explicitly derived. We show the interactions between vector breathers and vector solitons.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nat. Photonics 8, 755–764 (2014)

    Article  Google Scholar 

  2. Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N., Dudley, J.M.: The Peregrine soliton in nonlinear fibre optics. Nat. Phys. 6, 790–795 (2010)

    Article  Google Scholar 

  3. Osborne, A.R.: Nonlinear Ocean Waves. Acad, New York (2009)

    Google Scholar 

  4. Baronio, F., Conforti, M., Degasperis, A., Lombardo, S.: Rogue waves emerging from the resonant interaction of three waves. Phys. Rev. Lett. 111, 114101 (2013)

    Article  Google Scholar 

  5. Wazwaz, A.M.: Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities. Nonlinear Dyn. 83, 591–596 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wazwaz, A.M.: Multiple soliton solutions and multiple complex soliton solutions for two distinct Boussinesq equations. Nonlinear Dyn. 85, 731–737 (2016)

    Article  MathSciNet  Google Scholar 

  7. Lü, X.: Madelung fluid description on a generalized mixed nonlinear Schrödinger equation. Nonlinear Dyn. 81, 239–247 (2015)

    Article  MATH  Google Scholar 

  8. Lü, X., Peng, M.: Nonautonomous motion study on accelerated and decelerated solitons for the variable-coefficient Lenells–Fokas model. Chaos 23, 013122 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dai, C.Q., Wang, Y.Y.: Controllable combined Peregrine soliton and Kuznetsov–Ma soliton in PT-symmetric nonlinear couplers with gain and loss. Nonlinear Dyn. 80, 715 (2015)

    Article  MathSciNet  Google Scholar 

  10. Zhu, H.P.: Spatiotemporal solitons on cnoidal wave backgrounds in three media with different distributed transverse diffraction and dispersion. Nonlinear Dyn. 76, 1651 (2014)

    Article  MathSciNet  Google Scholar 

  11. Guo, R., Liu, Y.F., Hao, H.Q., Qi, F.H.: Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium. Nonlinear Dyn. 80, 1221 (2015)

    Article  MathSciNet  Google Scholar 

  12. Liu, W.J., Lin, X.C., Lei, M.: Soliton amplification in inhomogeneous optical waveguides. J. Mod. Opt. 60, 932–935 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, L., Wang, Z.Z., Jiang, D.Y., Qi, F.H., Guo, R.: Semirational solutions and baseband modulational instability of the AB system in fluid mechanics. Eur. Phys. J. Plus 130, 199 (2015)

    Article  Google Scholar 

  14. Kibler, B., Fatome, J., et al.: Observation of Kuznetsov–Ma soliton dynamics in optical fibre. Sci. Rep. 2, 463 (2012)

    Article  Google Scholar 

  15. Frisquet, B., Kibler, B., Millot, G.: Collision of Akhmediev breathers in nonlinear fiber optics. Phys. Rev. X 3, 041032 (2013)

    Google Scholar 

  16. Ghosh, S., Chakrabarti, N.: Nonlinear wave collapse, shock, and breather formation in an electron magnetohydrodynamic plasma. Phys. Rev. E 90, 063111 (2014)

    Article  Google Scholar 

  17. El-Tantawy, S.A., Wazwaz, A.M., Ali Shan, S.: On the nonlinear dynamics of breathers waves in electronegative plasmas with Maxwellian negative ions. Phys. Plasmas 24, 022105 (2017)

    Article  Google Scholar 

  18. Manikandan, K., Muruganandam, P., Senthilvelan, M., Lakshmanan, M.: Manipulating matter rogue waves and breathers in Bose–Einstein condensates. Phys. Rev. E 90, 062905 (2014)

    Article  Google Scholar 

  19. Chowdury, A., Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions. Phys. Rev. E 91, 022919 (2015)

    Article  MathSciNet  Google Scholar 

  20. Chowdury, A., Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Breather-to-soliton conversions described by the quintic equation of the nonlinear Schrödinger hierarchy. Phys. Rev. E 91, 032928 (2015)

    Article  MathSciNet  Google Scholar 

  21. Chowdury, A., Ankiewicz, A., Akhmediev, N.: Moving breathers and breather-to-soliton conversions for the Hirota equation. Proc. R. Soc. A 471, 20150130 (2015)

  22. Wang, L., Zhang, J., et al.: Breather-to-soliton transitions, nonlinear wave interactions, and modulational instability in a higher-order generalized nonlinear Schrödinger equation. Phys. Rev. E 93, 012214 (2016)

    Article  Google Scholar 

  23. Agrawal, G.P.: Nonlinear Fiber Optics, 5th edn. Academic Press, London (2012)

    MATH  Google Scholar 

  24. Porsezian, K., Nakkeeran, K.: Optical soliton propagation in an erbium doped nonlinear light guide with higher order dispersion. Phys. Rev. Lett. 74, 2941 (1995)

    Article  Google Scholar 

  25. Wang, L., et al.: Asymmetric Rogue waves, breather-to-soliton conversion, and nonlinear wave interactions in the Hirota–Maxwell–Bloch system. J. Phys. Soc. Jpn. 85, 024001 (2016)

    Article  Google Scholar 

  26. Wang, Q.M., Gao, Y.T., Su, C.Q., Zuo, D.W.: Solitons, breathers and rogue waves for a higher-order nonlinear Schrödinger Maxwell–Bloch system in an erbium-doped fiber system. Phys. Scr. 90, 105202 (2015)

    Article  Google Scholar 

  27. Mahnke, Ch., Mitschke, F.: Possibility of an Akhmediev breather decaying into solitons. Phys. Rev. A 85, 033808 (2012)

    Article  Google Scholar 

  28. Yang, Y., Yan, Z., Malomed, B.A.: Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation. Chaos 25, 103112 (2015)

    Article  MathSciNet  Google Scholar 

  29. Boudebs, G., Cherukulappurath, S., Leblond, H., Troles, J., Smektala, F., Sanchez, F.: Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses. Opt. Commun. 219, 427–433 (2003)

    Article  Google Scholar 

  30. Baronio, F., De Angelis, C., Marangoni, M., Manzoni, C., Ramponi, R., Cerullo, G.: Spectral shift of femtosecond pulses in nonlinear quadratic PPSLT crystals. Opt. Express 14, 4774–4779 (2006)

    Article  Google Scholar 

  31. Conforti, M., Baronio, F., Trillo, S.: Dispersive shock waves in phase-mismatched second-harmonic generation. Opt. Lett. 37, 1082–1084 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

We express our sincere thanks to the Editor and Reviewers for the valuable comments. This work is supported by the Fundamental Research Funds for the Central Universities.

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Wen-Rong Sun

Authors
  1. Wen-Rong Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen-Rong Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, WR. Nonlinear localized wave conversions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system with quintic terms in an erbium-doped fiber. Nonlinear Dyn 89, 383–390 (2017). https://doi.org/10.1007/s11071-017-3460-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3460-y

Keywords

Search

Navigation