Skip to main content
SpringerLink
Log in

Propagation of Solitons in Quasi-periodic Nonlinear Coupled Waveguides

  • Condensed Matter
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

This paper is a tribute to Professor Mahir Saleh Hussein. It is motivated by two works which we published in collaboration in Cardoso et al. (Phys. Lett. A 374, 2356 2010, 374, 4594 2010). Here, we study the propagation of solitons in nonlinear coupled waveguides described by coupled nonlinear Schrödinger equations. In a specific case, these coupled equations behave as an exactly integrable nonlinear system known as the Manakov model. We introduce quasi-periodic nonlinear couplings by merging the components that allow changing the nonlinearities of the system, and study how the quasi-periodic nonlinearities modify the behavior of the solutions.

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. G.P. Kivshar, Y. Agrawal. Optical Solitons: From Fibers to Photonic Crystals (Academic Press, New York, 2003)

    Google Scholar 

  2. S. Pitaevski, L.P. Stringari. Bose-Einstein Condensation (Oxford University Press, Oxford, 2003)

    MATH  Google Scholar 

  3. H.-H. Chen, C.-S. Liu, . Phys. Rev. Lett. 37, 693 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  4. A.R. Osborne, E. Segre, G. Boffetta, L. Cavaleri, . Phys. Rev. Lett. 67, 592 (1991)

    Article  ADS  Google Scholar 

  5. W. Trillo, S. Torruellas (eds.), Spatial Solitons (Springer, Berlin, 2001)

    Google Scholar 

  6. G Assanto (ed.), Nemations: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, New Jersey, 2013)

    MATH  Google Scholar 

  7. M. Remoissenen. Waves Called Solitons (Springer, Berlin, 1999)

    Book  Google Scholar 

  8. A.T. Avelar, D. Bazeia, W.B. Cardoso, . Phys. Rev. E. 79, 025602 (2009)

    Article  ADS  Google Scholar 

  9. W.B. Cardoso, A.T. Avelar, D. Bazeia, . Nonlinear Anal.-Real World Appl. 11, 4269–4274 (2010)

    Article  MathSciNet  Google Scholar 

  10. A.T. Avelar, D. Bazeia, W.B. Cardoso, . Phys. Rev. E. 82, 057601 (2010)

    Article  ADS  Google Scholar 

  11. W.B. Cardoso, H.L.C. Couto, A.T. Avelar, D. Bazeia, . Commun. Nonlinear Sci. Numer. Simul. 48, 474 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  12. W.B. Cardoso, J. Zeng, A.T. Avelar, D. Bazeia, B.A. Malomed, . Phys. Rev. E. 88, 025201 (2013)

    Article  ADS  Google Scholar 

  13. L. Calaça, A.T. Avelar, D. Bazeia, W.B. Cardoso, . Commun. Nonlinear Sci. Numer. Simul. 19, 2928–2934 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  14. B.A. Malomed. Soliton Manegement in Periodic Systems (Springer, New York, 2006)

    Google Scholar 

  15. S.V. Manakov, . Sov. Phys. JETP. 38, 248 (1974)

    ADS  Google Scholar 

  16. S. Stalin, R. Ramakrishnan, M. Senthilvelan, M. Lakshmanan, . Phys. Rev. Lett. 122, 043901 (2019)

    Article  ADS  Google Scholar 

  17. Q.-H. Park, H.J. Shin, . Phys. Rev. E. 59, 2373 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  18. W.-R. Sun, B. Tian, Y. Jiang, H.-L. Zhen, . Phys. Rev. E. 91, 023205 (2015)

    Article  ADS  Google Scholar 

  19. T. Kanna, M. Lakshmanan, . Phys. Rev. Lett. 86, 5043 (2001)

    Article  ADS  Google Scholar 

  20. T. Kanna, M. Lakshmanan, . Phys. Rev. E. 67, 046617 (2003)

    Article  ADS  Google Scholar 

  21. W.B. Cardoso, A.T. Avelar, D. Bazeia, . Phys. Rev. E. 86, 027601 (2012)

    Article  ADS  Google Scholar 

  22. J. Ma, G.D. Shao, Y.F. Song, L.M. Zhao, Y.J. Xiang, D.Y. Shen, M. Richardson, D.Y. Tang, . Opt. Lett. 44, 2185 (2019)

    Article  ADS  Google Scholar 

  23. X. Hu, J. Guo, G.D. Shao, Y.F. Song, S.W. Yoo, B.A. Malomed, D.Y. Tang, . Opt. Express. 27, 18311 (2019)

    Article  ADS  Google Scholar 

  24. X. Hu, J. Guo, G.D. Shao, Y.F. Song, L.M. Zhao, L. Li, D.Y. Tang, . Phys. Rev. A. 101, 063807 (2020)

    Article  ADS  Google Scholar 

  25. W.B. Cardoso, A.T. Avelar, D. Bazeia, M.S. Hussein, . Phys. Lett. A. 374, 2356 (2010)

    Article  ADS  Google Scholar 

  26. W. Cardoso, S. Leão, A. Avelar, D. Bazeia, M. Hussein, . Phys. Lett. A. 374, 4594 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  27. W. Cardoso, A. Avelar, D. Bazeia, . Phys. Lett. A. 374, 2640 (2010)

    Article  ADS  Google Scholar 

  28. S. Manakov, . Sov. J. Exp. Theor. Phys. 38, 248 (1974)

    ADS  Google Scholar 

  29. S. Novikov, S.V. Manakov, L.P. Pitaevskii, V.E. Zakharov. Theory of Solitons: The Inverse Scattering Method Monographs in Contemporary Mathematics (Springer, US, 1984)

    MATH  Google Scholar 

  30. N. Lazarides, G.P. Tsironis, . Phys. Rev. E. 71, 036614 (2005)

    Article  ADS  Google Scholar 

  31. T. Kanna, M. Lakshmanan, P. Tchofo Dinda, Nail Akhmediev, . Phys. Rev. E. 73, 026604 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  32. V.M. Pérez-García, J. Belmonte Beitia, . Phys. Rev. A. 72, 033620 (2005)

    Article  ADS  Google Scholar 

  33. S. Inouye, J. Goldwin, M.L. Olsen, C. Ticknor, J.L. Bohn, D.S. Jin, . Phys. Rev. Lett. 93, 183201 (2004)

    Article  ADS  Google Scholar 

  34. C.A. Stan, M.W. Zwierlein, C.H. Schunck, S.M.F. Raupach, W. Ketterle, . Phys. Rev. Lett. 93, 143001 (2004)

    Article  ADS  Google Scholar 

  35. Y. Cheng, S.K. Adhikari, . Phys. Rev. A. 84, 053634 (2011)

    Article  ADS  Google Scholar 

  36. B. Kerr, M.A. Riley, M.W. Feldman, B.J.M. Bohannan, . Nature. 418, 171 (2002)

    Article  ADS  Google Scholar 

Download references

Funding

The authors acknowledge the financial support of the Brazilian agencies CNPq (#312723/2018-0, #425718/2018-2, #404913/2018-0, #303469/2019-6 & #306065/2019-3), CAPES (PROCAD 2013), and FAPEG (PRONEM #201710267000540, PRONEX #201710267000503). This work was also performed as part of the Brazilian National Institute of Science and Technology (INCT) for Quantum Information (#465469/2014-0). It was also supported by Paraiba State Research Foundation, FAPESQ-PB Grant no. 0015/2019.

Author information

Authors and Affiliations

  1. Instituto de Física, Universidade Federal de Goiás, Goiânia, Goiás, 74.690-900, Brazil

    Wesley Bueno Cardoso & Ardiley Torres Avelar

  2. Departamento de Física, Universidade Federal da Paraíba, João Pessoa, Paraíba, 58051-970, Brazil

    Dionisio Bazeia

Authors
  1. Wesley Bueno Cardoso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ardiley Torres Avelar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dionisio Bazeia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dionisio Bazeia.

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

Cardoso, W.B., Avelar, A.T. & Bazeia, D. Propagation of Solitons in Quasi-periodic Nonlinear Coupled Waveguides. Braz J Phys 51, 151–156 (2021). https://doi.org/10.1007/s13538-020-00836-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-020-00836-w

Keywords

Search

Navigation