Skip to main content
SpringerLink
Log in

M-lump and lump–kink solutions of \((2+1)\)-dimensional Caudrey–Dodd-Gibbon–Kotera–Sawada equation

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper, M-lump and interaction between lumps and kink solitons of the \((2+1)\)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation are studied based on Hirota bilinear form. M-lump solutions are derived by taking a ‘long wave’ limit of the N-soliton solutions, and the lump–kink solutions are presented consequently. In addition, evolutions of solutions are shown by choosing certain parameters.

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. S V Manakov, V E Zakharov, L A Bordag, A R Its and V B Matveev, Phys. Lett. A 63(3), 205 (1977)

    Article  ADS  Google Scholar 

  2. W X Ma, Phys. Lett. A 379(36), 1975 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  3. W X Ma, Y Zhou and R Dougherty, Int. J. Mod. Phys. B 30, 1640018 (2016)

  4. W X Ma and Y Zhou, J. Differ. Equ. 264(4), 2633 (2018)

    Article  ADS  Google Scholar 

  5. J G Liu, J Q Du, Z F Zeng and B Nie, Nonlinear Dyn. 88(1), 655 (2017)

    Article  Google Scholar 

  6. J G Liu, J Q Du, Z F Zeng and G P Ai, Chaos 26(10), 103114 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  7. K Roy, S K Ghosh and P Chatterjee, Pramana – J. Phys. 86, 873 (2016)

    Article  ADS  Google Scholar 

  8. W Tan, H P Dai, Z D Dai and W Y Zhong, Pramana – J. Phys. 89: 77 (2017)

    Article  ADS  Google Scholar 

  9. K Imai, Prog. Theor. Phys. 98(5), 1013 (1997)

    Article  ADS  Google Scholar 

  10. H D Wahlquist and F B Estabrook, Phys. Rev. Lett. 31, 1386 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  11. W X Ma and A Abdeljabbar, Appl. Math. Lett. 12, 1500 (2012)

    Article  Google Scholar 

  12. J Villarroel and M J Ablowitz, Commun. Math. Phys. 207(1), 1 (1999)

    Article  ADS  Google Scholar 

  13. A S Fokas and M J Ablowitz, J. Math. Phys. 25, 2494 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  14. J Satsuma and M J Ablowitz, J. Math. Phys. 20(7), 1496 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  15. Y Zhang, Y P Liu and X Y Tang, Nonlinear Dyn. 93, 2533 (2018)

    Article  Google Scholar 

  16. J Rao, Y Cheng and J He, Stud. Appl. Math. 139(4), 568 (2017)

    Article  MathSciNet  Google Scholar 

  17. H Q Zhao and W X Ma, Comput. Math. Appl. 74, 1399 (2017)

    Article  MathSciNet  Google Scholar 

  18. H Q Sun and A H Chen, Appl. Math. Lett. 68, 55 (2017)

    Article  MathSciNet  Google Scholar 

  19. J G Liu and Y He, Nonlinear Dyn. 92(3), 1103 (2018)

    Article  Google Scholar 

  20. J E Liu and Y F Zhang, Results Phys. 10, 94 (2018)

    Article  ADS  Google Scholar 

  21. X E Zhang and Y Chen, Nonlinear Dyn. 1, 755 (2017)

    Google Scholar 

  22. P J Caudrey, R K Dodd and J D Gibbon, Proc. R. Soc. Lond. A 351, 407 (1976)

    Article  ADS  Google Scholar 

  23. K Sawada and T Kotera, Prog. Theor. Phys. 51, 1355 (1974)

    Article  ADS  Google Scholar 

  24. B G Konopelchenko and V G Dubrovsky, Phys. Lett. A 102, 15 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  25. A M Wazwaz, Math. Meth. Appl. Sci. 34, 1580 (2011)

    Article  Google Scholar 

  26. C W Cao, Y T Wu and X G Geng, Phys. Lett. A 256, 59 (1999)

    Article  ADS  Google Scholar 

  27. Z H Deng, X Chang, J N Tan, B Tang and K Deng, Int. J. Theor. Phys. 58, 92 (2019)

    Article  Google Scholar 

  28. W Q Peng, S F Tian, L Zou and T T Zhang, Nonlinear Dyn. 93, 1841(2018)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos 11571049 and 11101048) and China Scholarship Council.

Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Jinchao Chen & Yezhou Li

Authors
  1. Jinchao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yezhou Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yezhou Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, J., Li, Y. M-lump and lump–kink solutions of \((2+1)\)-dimensional Caudrey–Dodd-Gibbon–Kotera–Sawada equation. Pramana - J Phys 94, 105 (2020). https://doi.org/10.1007/s12043-020-01974-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-020-01974-1

Keywords

PACS Nos

Search

Navigation