Skip to main content
SpringerLink
Log in

Breather-type solutions and rogue waves to a generalised (2\(+\)1)-dimensional nonlinear Schrödinger equation

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

The aim of this paper was to study a generalised (2\(+\)1)-dimensional nonlinear Schrödinger equation, which can give us many important mathematical and physical models to illustrate various nonlinear phenomena in physical and engineering sciences. Based on a general Hirota bilinear form, the breather-type and non-singular rational solutions are presented. Akhmediev breather and Ma breather solutions can be considered as solutions representing the nonlinear propagation of the unstable model. In addition, by means of the bilinear transformation method, the fundamental rogue waves are given in terms of the Grammian determinant, which are shown to be line rouge waves. It is then demonstrated that the non-singular rational solutions generated via the long wave limit approach cover the rogue waves presented by the bilinear transformation method. The results presented in this paper exhibit the complexity and diversity of dynamical behaviour for the considered complex system.

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. M J Ablowitz and J Satsuma, J. Math. Phys. 19, 2180 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  2. J Satsuma and M J Ablowitz, J. Math. Phys. 20, 1496 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  3. N Akhmediev, A Ankiewicz and M Taki, Phys. Lett. A 373, 675 (2009)

    Article  ADS  Google Scholar 

  4. W X Ma, S Manukure, H Wang and S Batwa, Mod. Phys. Lett. B 35, 2150160 (2021)

    Article  ADS  Google Scholar 

  5. W X Ma and L Q Zhang, Pramana – J. Phys. 94, 43 (2020)

    Article  ADS  Google Scholar 

  6. Y H Yin, S J Chen and X Lü, Chin. Phys. B 29, 120502 (2020)

    Article  ADS  Google Scholar 

  7. H Q Zhang and J Chen, Mod. Phys. Lett. B 30, 1650106 (2016)

    Article  ADS  Google Scholar 

  8. Y Ohta and J K Yang, Phys. Rev. E 86, 036604 (2012)

    Article  ADS  Google Scholar 

  9. Y Ohta and J K Yang, J. Phys. A Math. Theor. 46, 105202 (2013)

    Article  ADS  Google Scholar 

  10. Y Ohta and J K Yang, Proc. R. Soc. Lond. Ser. A 468, 1716 (2012)

    ADS  Google Scholar 

  11. X Lü, S J Chen, G Z Liu and W X Ma, E. Asian J. Appl. Math. 11, 594 (2021)

    Article  Google Scholar 

  12. N Akhmediev, A Ankiewicz and J M Soto-Crespo, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 026601 (2009)

    Article  Google Scholar 

  13. K Dysthe, H E Krogstad and P Mller, Annu. Rev. Fluid Mech. 40, 287 (2008)

    Article  ADS  Google Scholar 

  14. V E Zakharov and A I Dyachenko, Eur. J. Mech. B 29, 127 (2010)

    Article  Google Scholar 

  15. K Dysthe and K Trulsen, Phys. Scr. 82, 48 (1999)

    Article  Google Scholar 

  16. H Gao, Pramana – J. Phys. 88, 84 (2017)

    Article  ADS  Google Scholar 

  17. B N Sun and Z Lian, Pramana – J. Phys. 90, 23 (2018)

    Article  ADS  Google Scholar 

  18. B L Guo and L M Ling, Chin. Phys. Lett. 28, 4 (2011)

    Google Scholar 

  19. L H Wang, K Porsezian and J S He, Phys. Rev. E 87, 053202 (2013)

    Article  ADS  Google Scholar 

  20. X Guo Geng, Y H Li and B Xue, Nonlinear Dyn. 105, 2575 (2021)

    Article  Google Scholar 

  21. W X Ma, Y S Bai and A Adjiri, Eur. Phys. J. Plus 136, 240 (2021)

    Article  Google Scholar 

  22. S H Chen, Phys. Lett. A 378, 1095 (2014)

    Article  ADS  Google Scholar 

  23. L Cheng and Y Zhang, Mod. Phys. Lett. B 31, 1750224 (2017)

    Article  ADS  Google Scholar 

  24. J W Xia, Y W Zhao and X Lü, Commun. Nonlinear Sci. Numer. Simul. 90, 105260 (2020)

    Article  MathSciNet  Google Scholar 

  25. N V Priya, M Senthilvelan and M Lakshmanan, Pramana – J. Phys. 84, 339 (2015)

    Article  ADS  Google Scholar 

  26. M Tajiri and T Arai, Proc. Inst. Math. NAS Ukraine 30, 210 (2000)

    Google Scholar 

  27. A S Fokas, Inverse Probl. 10, L19 (1994)

    Article  ADS  Google Scholar 

  28. R Radha and M Lakshmanan, Chaos Solitons Fractals 8, 17 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  29. M Lakshmanan and R Radha, Pramana – J. Phys. 48, 163 (1997)

    Article  ADS  Google Scholar 

  30. A S Fokas and P M Santini, Physica D 44, 99 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  31. C R Gilson and J J C Nimmo, Proc. R. Soc. A 435, 339 (1991)

    ADS  Google Scholar 

  32. M Boiti, F Pempinelli and P C Sabatier, Inverse Probl. 9, 1 (1993)

    Article  ADS  Google Scholar 

  33. P M Santini and A S Fokas, Commun. Math. Phys. 115, 375 (1988)

    Article  ADS  Google Scholar 

  34. J G Rao, K Porsezian and J S He, Chaos 27, 083115 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  35. N Akhmediev, V M Eleonskii and N E Kulagin, Theor. Math. Phys. 72, 809 (1987)

    Article  Google Scholar 

  36. Y C Ma, Stud. Appl. Math. 60, 43 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  37. D H Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983)

    Article  Google Scholar 

  38. J G Rao, L H Wang, Y Zhang and J S He, Commun. Theor. Phys. 12, 605 (2015)

    Article  ADS  Google Scholar 

  39. J C Chen, Y Chen, B F Feng, K Maruno and Y Ohta, J. Phys. Soc. Jpn. 87, 094007 (2018)

    Article  ADS  Google Scholar 

  40. B N Sun and A M Wazwaz, Commun. Nonlinear Sci. Numer. Simul. 64, 1 (2018)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors express their sincere thanks to the referees and editors for their valuable comments.

Author information

Authors and Affiliations

  1. Normal School, Jinhua Polytechnic, Jinhua,  321007, Zhejiang, China

    Li Cheng

  2. Department of Mathematics, Zhejiang Normal University, Jinhua,  321004, Zhejiang, China

    Yi Zhang

Authors
  1. Li Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Cheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, L., Zhang, Y. Breather-type solutions and rogue waves to a generalised (2\(+\)1)-dimensional nonlinear Schrödinger equation. Pramana - J Phys 96, 52 (2022). https://doi.org/10.1007/s12043-022-02293-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-022-02293-3

Keywords

PACS Nos

Search

Navigation