Skip to main content
SpringerLink
Log in

Periodic soliton interactions for higher-order nonlinear Schrödinger equation in optical fibers

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

Abstract

Research on the interactions between optical solitons is of great significance for the large capacity and long distance transmission in optical fibers. In this paper, interactions between periodic solitons are investigated for the first time. Analytic solution for the high-order nonlinear Schrödinger equation, which can be used to describe the periodic soliton transmission, is obtained based on the bilinear method. Interaction characteristics between periodic solitons are discussed. Influences of corresponding dispersion and nonlinear effects on their interactions are analyzed. Results provide theoretical guidance for the stable transmission of periodic solitons in inhomogeneous optical fibers.

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

Similar content being viewed by others

References

  1. Wazwaz, A.M.: Multiple-soliton solutions for a (3 + 1)-dimensional generalized KP equation. Commun. Nonlinear Sci. Numer. Simul. 17(2), 491–495 (2012)

    Article  MathSciNet  Google Scholar 

  2. Wazwaz, A.M., El-Tantawy, S.A.: A new(3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation. Nonlinear Dyn. 84(2), 1107–1112 (2016)

    Article  MathSciNet  Google Scholar 

  3. Wazwaz, A.M.: Multiple soliton solutions and multiple complex soliton solutions for two distinct Boussinesq equations. Nonlinear Dyn. 85(2), 731–737 (2016)

    Article  MathSciNet  Google Scholar 

  4. Wazwaz, A.M., El-Tantawy, S.A.: A new integrable (3 + 1)-dimensional KdV-like model with its multiple-soliton solutions. Nonlinear Dyn. 83, 1529–1534 (2016)

    Article  MathSciNet  Google Scholar 

  5. Wazwaz, A.M.: Two-mode fifth-order KdV equations: necessary conditions for multiple-soliton solutions to exist. Nonlinear Dyn. 87(3), 1685–1691 (2017)

    Article  MathSciNet  Google Scholar 

  6. Wazwaz, A.M., El-Tantawy, S.A.: New (3 + 1)-dimensional equations of Burgers type and Sharma–Tasso–Olver type: multiple-soliton solutions. Nonlinear Dyn. 87(4), 2457–2461 (2017)

    Article  MathSciNet  Google Scholar 

  7. Qi, F.H., Huang, Y.H., Wang, P.: Solitary-wave and new exact solutions for an extended (3 + 1)-dimensional Jimbo–Miwa-like equation. Appl. Math. Lett. 100, 106004 (2020)

    Article  MathSciNet  Google Scholar 

  8. Wang, H.T., Wen, X.Y.: Dynamics of discrete soliton propagation and elastic interaction in a higher-order coupled Ablowitz–Ladik equation. Appl. Math. Lett. 100, 106013 (2020)

    Article  MathSciNet  Google Scholar 

  9. Xie, X.Y., Yang, S.K., Ai, C.H., Kong, L.C.: Integrable turbulence for a coupled nonlinear Schrödinger system. Phys. Lett. A 384, 126119 (2020)

    Article  Google Scholar 

  10. Zhao, Y.T., Ma, S.Y., Jiang, S.C., Yang, Y.J., Zhao, X., Chen, J.G.: All-optical reconstruction of k-dependent transition dipole moment by solid harmonic spectra from ultrashort laser pulses. Opt. Express 27, 34392–34403 (2019)

    Article  Google Scholar 

  11. Xie, X.Y., Meng, G.Q.: Dark solitons for a variable-coefficient AB system in the geophysical fluids or nonlinear optics. Eur. Phys. J. Plus 134, 359 (2019)

    Article  Google Scholar 

  12. Lan, Z.Z.: Rogue wave solutions for a coupled nonlinear Schrödinger equation in the birefringent optical fiber. Appl. Math. Lett. 98, 128–134 (2019)

    Article  MathSciNet  Google Scholar 

  13. Yan, Y.Y., Liu, W.J.: Stable transmission of solitons in the complex cubic-quintic Ginzburg–Landau equation with nonlinear gain and higher-order effects. Appl. Math. Lett. 98, 171–176 (2019)

    Article  MathSciNet  Google Scholar 

  14. Dai, C.Q., Fan, Y., Zhang, N.: Re-observation on localized waves constructed by variable separation solutions of (1 + 1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method. Appl. Math. Lett. 96, 20–26 (2019)

    Article  MathSciNet  Google Scholar 

  15. Zhang, Z., Yang, X.Y., Li, B.: Soliton molecules and novel smooth positons for the complex modified KdV equation. Appl. Math. Lett. 103, 106168 (2020)

    Article  MathSciNet  Google Scholar 

  16. Dong, J.J., Li, B., Yuen, M.W.: Soliton molecules and mixed solutions of the (2 + 1)-dimensional bidirectional Sawada–Kotera equation. Commun. Theor. Phys. 72, 25002 (2020)

    Article  Google Scholar 

  17. Zhang, Z., Yang, X.Y., Li, B.: Novel soliton molecules and breather-positon on zero background for the complex modified KdV equation. Nonlinear Dyn. (2020). https://doi.org/10.1007/s11071-020-05570-1

    Article  Google Scholar 

  18. Wang, B., Zhang, Z., Li, B.: Soliton molecules and some hybrid solutions for the nonlinear Schrödinger equation. Chin. Phys. Lett. 37, 030501 (2020)

    Article  Google Scholar 

  19. Zhang, Z., Yang, X.Y., Li, W.T., Li, B.: Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2 + 1)-dimensional Kadomtsev–Petviashvili equation. Chin. Phys. B 28, 110201 (2019)

    Article  Google Scholar 

  20. Liu, X., Liu, W., Triki, H., Zhou, Q., Biswas, A.: Periodic attenuating oscillation between soliton interactions for higher-order variable coefficient nonlinear Schrödinger equation. Nonlinear Dyn. 96, 801–809 (2019)

    Article  Google Scholar 

  21. Seadawy, A.R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability. Results Phys. 7, 43–48 (2017)

    Article  Google Scholar 

  22. Liu, W., Zhang, Y., Luan, Z., Zhou, Q., Mirzazadeh, M., Ekici, M., Biswas, A.: Dromion-like soliton interactions for nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers. Nonlinear Dyn. 96, 729–736 (2019)

    Article  Google Scholar 

  23. Dai, C.Q., Wang, Y.Y., Fan, Y., Zhang, J.F.: Interactions between exotic multi-valued solitons of the (2 + 1)-dimensional Korteweg–de Vries equation describing shallow water wave. Appl. Math. Model. 80, 506–515 (2020)

    Article  MathSciNet  Google Scholar 

  24. Liu, W., Zhang, Y., Wazwaz, A.M., Zhou, Q.: Analytic study on triple-S, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber. Appl. Math. Comput. 361, 325–331 (2019)

    Article  MathSciNet  Google Scholar 

  25. Dai, C.Q., Liu, J., Fan, Y., Yu, D.G.: Two-dimensional localized Peregrine solution and breather excited in a variable-coefficient nonlinear Schrödinger equation with partial nonlocality. Nonlinear Dyn. 88, 1373–1383 (2017)

    Article  Google Scholar 

  26. Dai, C.Q., Fan, Y., Wang, Y.Y.: Three-dimensional optical solitons formed by the balance between different-order nonlinearities and high-order dispersion/diffraction in parity-time symmetric potentials. Nonlinear Dyn. 98, 489–499 (2019)

    Article  Google Scholar 

  27. Chowdury, A., Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms. Phys. Rev. E 90, 032922 (2014)

    Article  Google Scholar 

  28. Liu, S., Zhou, Q., Biswas, A., Liu, W.: Phase-shift controlling of three solitons in dispersion-decreasing fibers. Nonlinear Dyn. 98, 395–401 (2019)

    Article  Google Scholar 

  29. Huang, Q.M.: Integrability and dark soliton solutions for a high-order variable coefficients nonlinear Schrödinger equation. Appl. Math. Lett. 93, 29–33 (2019)

    Article  MathSciNet  Google Scholar 

  30. Udaiyakumar, R., Ali, N.B., Naicker, B.M., Rajan, M.S.M., Yupapin, P., Amiri, I.S.: Analytical and numerical demonstration of phase characteristics on two solitons under the influence of third-order dispersion. Opt. Quantum Electron. 51, 163 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

We thank the support of the National Natural Science Foundation of China (11975012, 11905009), and the Outstanding Youth Project of Taizhou University (2019JQ002). This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. (KEP-64-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.

Author information

Author notes

  1. Jigen Chen and Qin Zhou have contributed equally to this work.

Authors and Affiliations

  1. Zhejiang Provincial Key Laboratory for Cutting Tools, Taizhou University, Taizhou, 318000, China

    Jigen Chen

  2. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing, 100876, China

    Zitong Luan & Wenjun Liu

  3. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, China

    Qin Zhou

  4. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdullah Kamis Alzahrani & Anjan Biswas

  5. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL, 35762-4900, USA

    Anjan Biswas

  6. Department of Applied Mathematics, National Research Nuclear University, Kashirskoe Shosse, Moscow, Russian Federation, 115409

    Anjan Biswas

  7. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, 0008, South Africa

    Anjan Biswas

Authors
  1. Jigen Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zitong Luan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abdullah Kamis Alzahrani
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anjan Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Wenjun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qin Zhou.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, J., Luan, Z., Zhou, Q. et al. Periodic soliton interactions for higher-order nonlinear Schrödinger equation in optical fibers. Nonlinear Dyn 100, 2817–2821 (2020). https://doi.org/10.1007/s11071-020-05649-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05649-9

Keywords

Search

Navigation