Skip to main content
SpringerLink
Log in

Phase-shift controlling of three solitons in dispersion-decreasing fibers

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

Abstract

Phase-shift controlling can attenuate the interactions between solitons and gives practical advantage in optical communication systems. For the variable-coefficient nonlinear Schrödinger equation, which can be imitated the transmission of solitons in the dispersion-decreasing fiber, analytic three solitons solutions are derived via the Hirota method. Based on the obtained solutions, influences of the second-order dispersion parameters and other related parameters in different function types on the soliton transmission are discussed. Results declare that phase-shift controlling of solitons in dispersion-decreasing fiber can be achieved when the dispersion function is Gaussian one. In addition, by adjusting the constraint value, propagation distance of solitons can be further extended. This may be useful in the optical logic devices and ultra-short pulse lasers.

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Wazwaz, A.M.: A study on a two-wave mode Kadomtsev–Petviashvili equation: conditions for multiple soliton solutions to exist. Math. Methods Appl. Sci. 40, 4128–4133 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wazwaz, A.M.: A two-mode modified KdV equation with multiple soliton solutions. Appl. Math. Lett. 70, 1–6 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wazwaz, A.M.: Abundant solutions of various physical features for the (2+1)-dimensional modified KdV-Calogero–Bogoyavlenskii–Schiff equation. Nonlinear Dyn. 89, 1727–1732 (2017)

    Article  MathSciNet  Google Scholar 

  5. Wazwaz, A.M., El-Tantawy, S.A.: Solving the (3+1)-dimensional KP-Boussinesq and BKP-Boussinesq equations by the simplified Hirota’s method. Nonlinear Dyn. 88, 3017–3021 (2017)

    Article  MathSciNet  Google Scholar 

  6. Wazwaz, A.M.: Multiple soliton solutions and other exact solutions for a two-mode KdV equation. Math. Methods Appl. Sci. 40, 2277–2283 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. Nawaz, B., Ali, K., Abbas, S.O., Rizvi, S.T.R., Zhou, Q.: Optical solitons for non-Kerr law nonlinear Schrödinger equation with third and fourth order dispersions. Chin. J. Phys. 60, 133–140 (2019)

    Article  Google Scholar 

  8. Rizvi, S.T.R., Ali, K., Hanif, H.: Optical solitons in dual core fibers under various nonlinearities. Mod. Phys. Lett. B 33(17), 1950189 (2019)

    Article  MathSciNet  Google Scholar 

  9. Rizvi, S.T.R., Afzal, I., Ali, K.: optical solitons for Triki–Biswas equation. Mod. Phys. Lett. B 33, 1950264 (2019)

    Article  MathSciNet  Google Scholar 

  10. Liu, X.Y., Triki, H., Zhou, Q., Liu, W.J., Biswas, A.: Analytic study on interactions between periodic solitons with controllable parameters. Nonlinear Dyn. 94, 1703–709 (2018)

    Article  Google Scholar 

  11. Zhang, Y.J., Yang, C.Y., Yu, W.T., Mirzazadeh, M., Zhou, Q., Liu, W.J.: Interactions of vector anti-dark solitons for the coupled nonlinear Schrödinger equation in inhomogeneous fibers. Nonlinear Dyn. 94, 1351–1360 (2018)

    Article  Google Scholar 

  12. Liu, J., Wang, Y.G., Qu, Z.S., Fan, X.W.: 2 \(\mu \)m passive Q-switched mode-locked \({\rm Tm}^{3+}\): \(YAP\) laser with single-walled carbon nanotube absorber. Opt. Laser Technol. 44(4), 960–962 (2012)

    Article  Google Scholar 

  13. Zhang, C., Liu, J., Fan, X.W., Peng, Q.Q., Guo, X.S., Jiang, D.P., Qian, X.B., Su, L.B.: Compact passive Q-switching of a diode-pumped Tm, Y: \({\rm CaF}_{2}\) laser near 2 \(\mu \)m. Opt. Laser Technol. 103, 89–92 (2018)

    Article  Google Scholar 

  14. Lin, M.X., Peng, Q.Q., Hou, W., Fan, X.W., Liu, J.: 1.3 \(\mu \)m Q-switched solid-state laser based on few-layer ReS\(_{2}\) saturable absorber. Opt. Laser Technol. 109, 90–93 (2019)

    Article  Google Scholar 

  15. Biswas, A., Yildirim, Y., Yasar, E., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical solitons with differential group delay and four-wave mixing using two integration procedures. Optik 167, 170–188 (2018)

    Article  Google Scholar 

  16. Zhang, N., Xia, T.C., Fan, E.G.: A Riemann–Hilbert approach to the Chen–Lee–Liu equation on the half line. Acta Math. Appl. Sin. 34(3), 493–515 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang, N., Xia, T.C., Jin, Q.Y.: N-Fold Darboux transformation of the discrete Ragnisco–Tu system. Adv. Differ. Equ. 2018, 302 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tao, M.S., Zhang, N., Gao, D.Z., Yang, H.W.: Symmetry analysis for three-dimensional dissipation Rossby waves. Adv. Differ. Equ. 2018, 300 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gu, J.Y., Zhang, Y., Dong, H.H.: Dynamic behaviors of interaction solutions of (3+1)-dimensional shallow mater wave equation. Comput. Math. Appl. 76(6), 1408–1419 (2018)

    Article  MathSciNet  Google Scholar 

  20. Liu, Y., Dong, H.H., Zhang, Y.: Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows. Anal. Math. Phys. 2018, 1–17 (2018)

    Google Scholar 

  21. Guo, M., Zhang, Y., Wang, M., Chen, Y.D., Yang, H.W.: A new ZK-ILW equation for algebraic gravity solitary waves in finite depth stratified atmosphere and the research of squall lines formation mechanism. Comput. Math. Appl. 143, 3589–3603 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yang, H.W., Chen, X., Guo, M., Chen, Y.D.: A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Nonlinear Dyn. 91, 2019–2032 (2018)

    Article  MATH  Google Scholar 

  23. Zhao, B.J., Wang, R.Y., Sun, W.J., Yang, H.W.: Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions. Adv. Differ. Equ. 2018, 42 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lu, C., Fu, C., Yang, H.W.: Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions. Appl. Math. Comput. 327, 104–116 (2018)

    MathSciNet  MATH  Google Scholar 

  25. Biswas, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Ekici, M., Zhou, Q., Belic, M.: Optical soliton perturbation with Fokas–Lenells equation using three exotic and efficient integration schemes. Optik 165, 288–294 (2018)

    Article  Google Scholar 

  26. Triki, H., Biswas, A., Zhou, Q., Mirzazadeh, M., Mahmood, M.F., Moshokoa, S.P., Belic, M.: Solitons in optical metamaterials having parabolic law nonlinearity with detuning effect and Raman scattering. Optik 164, 606–609 (2018)

    Article  Google Scholar 

  27. Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83(1–2), 731–738 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Ekici, M., Mirzazadeh, M., Eslami, M.: Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion. Nonlinear Dyn. 84(2), 669–676 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Li, X.Z., Yan, X., Li, Y.S.: Investigation of multi-soliton, multi-cuspon solutions to the Camassa–Holm equation and their interaction. Chin. Ann. Math. Ser. B 33(2), 225–246 (2012)

    Article  MathSciNet  Google Scholar 

  30. Sun, K., Tian, B., Liu, W.J., Jiang, Y., Qu, Q.X., Wang, P.: Soliton dynamics and interaction in the Bose–Einstein condensates with harmonic trapping potential and time-varying interatomic interaction. Nonlinear Dyn. 67(1), 165–175 (2012)

    Article  MATH  Google Scholar 

  31. Askari, A., Javidan, K.: Interaction of noncommutative solitons with defects. Braz. J. Phys. 38(4), 610–614 (2008)

    Article  Google Scholar 

  32. Konyukhov, A.I., Dorokhova, M.A., Melnikov, L.A.E., Plastun, A.S.: Controlling the interaction between optical solitons using periodic dispersion variations in an optical fibre. Quantum Electron. 45(11), 1018–1022 (2015)

    Article  Google Scholar 

  33. Li, Y.G., She, W.L., Wang, H.C.: Perpendicular all-optical control of interactional optical spatical soliton pair. Acta Phys. Sin. 56(4), 2229–2236 (2007)

    Google Scholar 

  34. Shou, Q., Wu, M., Guo, Q.: Large phase shift of (1+1)-dimensional nonlocal spatial solitons in lead glass. Opt. Commun. 338, 133–137 (2015)

    Article  Google Scholar 

  35. Roy, K., Ghosh, S.K., Chatterjee, P.: Two-soliton and three-soliton interactions of electron acoustic waves in quantum plasma. Pramana 86(4), 873–883 (2016)

    Article  Google Scholar 

  36. Sun, Q.H., Pan, N., Lei, M., Liu, W.J.: Study on phase-shift control in dispersion decreasing fibers. Acta Phys. Sin. 63(15), 150506 (2014)

    Google Scholar 

  37. Zheng, H.J., Wu, C., Wang, Z., Yu, H., Liu, S., Li, X.: Propagation characteristics of chirped soliton in periodic distributed amplification systems with variable coefficients. Optik 123(9), 818–822 (2012)

    Article  Google Scholar 

  38. Zolotovskii, I.O., Sementsov, D.I.: Formation of the amplification regime of quasi-soliton pulses in waveguides with longitudinally inhomogeneous cross sections. Opt. Spectrosc. 102(4), 594–598 (2007)

    Article  Google Scholar 

  39. Yang, C.Y., Li, W.Y., Yu, W.T., Liu, M.L., Zhang, Y.J., Ma, G.L., Lei, M., Liu, W.J.: Amplification, reshaping, fission and annihilation of optical solitons in dispersion-decreasing fiber. Nonlinear Dyn. 92(2), 203–213 (2018)

    Article  MATH  Google Scholar 

  40. Liu, W.J., Zhang, Y.J., Pang, L.H., Yan, H., Ma, G.L., Lei, M.: Study on the control technology of optical solitons in optical fibers. Nonlinear Dyn. 86(2), 1069–1073 (2016)

    Article  Google Scholar 

  41. Pelusi, M.D., Liu, H.F.: Higher order soliton pulse compression in dispersion-decreasing optical fibers. IEEE J. Quantum Electron. 33(8), 1430–1439 (1997)

    Article  Google Scholar 

Download references

Acknowledgements

The work of Wenjun Liu was supported by the National Natural Science Foundation of China (Grant Nos. 11674036 and 11875008), by the Beijing Youth Top-notch Talent Support Program (Grant No. 2017000026833ZK08) and by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Grant No. IPOC2017ZZ05).

Author information

Authors and Affiliations

  1. 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

    Suzhi Liu & Wenjun Liu

  2. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China

    Qin Zhou

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

    Anjan Biswas

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

    Anjan Biswas

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

    Anjan Biswas

Authors
  1. Suzhi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anjan Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenjun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenjun Liu.

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

Liu, S., Zhou, Q., Biswas, A. et al. Phase-shift controlling of three solitons in dispersion-decreasing fibers. Nonlinear Dyn 98, 395–401 (2019). https://doi.org/10.1007/s11071-019-05200-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05200-5

Keywords

Search

Navigation