Skip to main content
SpringerLink
Log in

Lump-type solutions and interaction phenomenon to the bidirectional Sawada–Kotera equation

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper, we use the Hirota bilinear method. With the help of symbolic calculation and applying this method, we solve the \((2+1)\)-dimensional bidirectional Sawada–Kotera (bSK) equation to obtain some new lump-kink, lump-solitons, periodic kink-wave, periodic soliton and periodic wave 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
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. S L Jia, Y T Gao, C C Ding and G F Deng, Appl. Math. Lett. 74, 193 (2017)

    Article  MathSciNet  Google Scholar 

  2. B G Konopelcheno and V G Dubrovsky, Phys. Lett. A 102, 15 (1984)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. U Göktas and W Hereman, J. Symbolic Comput. 11, 1 (2008)

    Google Scholar 

  5. A M Wazwaz, Appl. Math. Comput. 184, 1002 (2007)

    MathSciNet  Google Scholar 

  6. M Y Ali, M G Hafez, M K H Chowdury and M T Akter, J. Appl. Math. Phys. 4, 262 (2016)

    Article  Google Scholar 

  7. A Salas, Appl. Math. Comput. 196, 812 (2008)

    MathSciNet  Google Scholar 

  8. C A Gómez and A H Salas, Appl. Math. Comput. 217, 1408 (2010)

    MathSciNet  Google Scholar 

  9. W R Shan, T Z Yan, X Lu, M Li and B Tian, Commun. Nonlinear Sci. Numer. Simul. 18, 1568 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  10. C Rogers, W K Schief and M P Stallybrass, Int. J. Non-Linear Mech. 30, 223 (1995)

    Article  Google Scholar 

  11. V G Dubrovsky and Y V Lisitsyn, Phys. Lett. A 295, 198 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  12. X Lü, T Geng, C Zhang, H W Zhu, X H Meng and B Tian, J. Mod. Phys. B 23, 5003 (2009)

    Article  ADS  Google Scholar 

  13. X Lü, B Tian, K Sun and P Wang, J. Math. Phys. 51, 113506 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  14. A M Wazwaz, Math. Method Appl. Sci. 34, 1580 (2011)

    Article  ADS  Google Scholar 

  15. L L Huang and Y Chen, Commun. Theor. Phys. 67, 473 (2017)

    Article  ADS  Google Scholar 

  16. A R Adem and X Lü, Nonlinear Dyn. 84, 915 (2016)

    Article  Google Scholar 

  17. D W Zuo, H X Mo and H P Zhou, Z. Naturforsch. A 71, 305 (2016)

  18. J Lv and S Bilige, Nonlinear Dyn. 90, 2119 (2017)

    Article  Google Scholar 

  19. J M Dye and A Parker, J. Math. Phys. 43, 4921 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  20. Y L Ma and X G Geng, Appl. Math. Comput. 218, 6963 (2012)

    MathSciNet  Google Scholar 

  21. X J Lai and X O Cai, Z. Naturforsch. A 65, 658 (2010)

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. H Q Zhao and W X Ma, Comput. Math. Appl. 74(6), 1399 (2017)

    Article  MathSciNet  Google Scholar 

  25. J Y Yang and W X Ma, Int. J. Mod. Phys. B 30, 1640028 (2016)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  27. W X Ma, Z Y Qin and X Lv, Nonlinear Dyn. 84, 923 (2016)

    Article  Google Scholar 

  28. C J Wang, Nonlinear Dyn. 84, 697 (2016)

    Article  Google Scholar 

  29. C J Wang, Z D Dai and C F Liu, Mediterr. J. Math. 13, 1087 (2016)

    Article  MathSciNet  Google Scholar 

  30. J Lü, S Bilige and T Chaolu, Nonlinear Dyn. 91, 1669 (2018)

    Article  Google Scholar 

  31. Y Zhang et al, Comput. Math. Appl. 73, 246 (2017)

    Article  MathSciNet  Google Scholar 

  32. X Zhang and Y Chen, Commun. Nonlinear Sci. Numer. Simul. 52, 24 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  33. M R Foroutan, J Manafian and A Ranjbaran, Nonlinear Dyn. 92, 2077 (2018)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. S T Chen and W X Ma, Front. Math. China 13, 525 (2018)

    Article  MathSciNet  Google Scholar 

  36. J B Zhang and W X Ma, Anal. Math. Phys. 74, 591 (2017)

    Google Scholar 

  37. J Y Yang, W X Ma and Z Y Qin, Anal. Math. Phys. 8, 427 (2018)

    Article  MathSciNet  Google Scholar 

  38. W X Ma, X L Yong and H Q Zhang, Comput. Math. Appl. 75, 289 (2018)

    Article  MathSciNet  Google Scholar 

  39. W X Ma, Integrability, in: Encyclopedia of nonlinear science edited by A Scott (Taylor & Francis, New York, 2005), pp. 250–253

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

    Article  ADS  Google Scholar 

  41. G Mu, Z Dai and Z Zhao, Pramana – J. Phys. 81, 367 (2013)

    Article  ADS  Google Scholar 

  42. Z Du, B Tian, X Y Xie, J Chai and X Y Wu, Pramana – J. Phys. 90: 45 (2018)

    Article  ADS  Google Scholar 

  43. W Tan, H Dai, Z Dai and W Zhong, Pramana – J. Phys. 89: 77 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. S Zhang, C Tian and W Y Qian, Pramana – J. Phys. 86, 1259 (2016)

    Article  ADS  Google Scholar 

  46. S H Seyedi, B N Saray and A Ramazani, Powder Technol.  340, 264 (2018)

    Article  Google Scholar 

  47. S H Seyedi, B N Saray and M R H Nobari, Appl. Math. Comput. 269, 488 (2015)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the research support provided by the Iran National Science Foundation and the support of the University of Tabriz under Grant Number 95007368.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Jalil Manafian & Mehrdad Lakestani

Authors
  1. Jalil Manafian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehrdad Lakestani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jalil Manafian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manafian, J., Lakestani, M. Lump-type solutions and interaction phenomenon to the bidirectional Sawada–Kotera equation. Pramana - J Phys 92, 41 (2019). https://doi.org/10.1007/s12043-018-1700-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-018-1700-4

Keywords

PACS Nos

Search

Navigation