Skip to main content
SpringerLink
Log in

Patterns of propagation of high-order nonlinear dispersion wave modelled by the generalised KP equation

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

A wide range of two-dimensional nonlinear wave is described by Kadomtsev–Petviashvili (KP) equation. We obtained the classification of travelling wave patterns to the generalised KP equation with high-order nonlinear dispersive and dissipative terms. Among these patterns, some new phenomena can be acquired for the first time. Representations of wave propagation patterns were achieved by taking specific values of parameters. This means that all these patterns can be realised under appropriate physical conditions.

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. B B Kadomtsev and V I Petviashvili, Sov. Phys. Dokl. 15, 539 (1970)

    ADS  Google Scholar 

  2. P Rosenau, Phys. Lett. A 275(3), 193 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  3. A M Wazwaz, Chaos Solitons Fractals 13, 1052 (2002)

    ADS  Google Scholar 

  4. M Song and Y L Ge, Comput. Math. Appl. 60, 1220 (2010)

    Article  MathSciNet  Google Scholar 

  5. A M Wazwaz, Appl. Math. Comput. 200, 160 (2008)

    MathSciNet  Google Scholar 

  6. C S Liu, Commun. Theor. Phys. 45(3), 395 (2006)

    Article  ADS  Google Scholar 

  7. C S Liu, Commun. Theor. Phys. 45(2), 219 (2006)

    Article  ADS  Google Scholar 

  8. C S Liu, Found. Phys. 41, 793 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  9. C S Liu, Acta Phys. Sin. 54(6), 2505 (2005)

    Google Scholar 

  10. C S Liu, Acta Phys. Sin. 54(10), 4506 (2005)

    Google Scholar 

  11. Y Liu, Appl. Math. Comput. 217, 5866 (2011)

    MathSciNet  Google Scholar 

  12. Y Liu and X Wang, Adv. Differ. Equ. 2019(1), 134 (2019)

    Article  Google Scholar 

  13. W H Li and Y Wang, Adv. Differ. Equ. 2019(1), 451 (2019)

    Article  Google Scholar 

  14. Y Pandir, Y Gurefe and E Misirli, Phys. Scr. 87, 025003 (2013)

    Article  ADS  Google Scholar 

  15. C S Liu, Chaos Solitons Fractals 42, 441 (2009)

    Article  ADS  Google Scholar 

  16. B Zheng et al, Physica A 532, 121780 (2019)

    Article  MathSciNet  Google Scholar 

  17. C S Liu, Chaos Solitons Fractals 40, 708 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  18. I Aslan, Appl. Math. Comput. 219, 2825 (2012)

    MathSciNet  Google Scholar 

  19. W X Ma and Z N Zhu, Appl. Math. Comput. 218, 11871 (2012)

    MathSciNet  Google Scholar 

  20. B Ghanbari and J Liu, Pramana – J. Phys. 94: 21 (2020)

    Article  ADS  Google Scholar 

  21. Y Chen, Z Yan and H Zhan, Phys. Lett. A 307, 107 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  22. M Khalfallah, Commun. Nonlinear Sci. Numer. Simulat. 14, 1169 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. A M Wazwaz, Commun. Nonlinear Sci. Numer. Simulat. 17, 491 (2012)

    Article  ADS  Google Scholar 

  24. L L Huang, Y F Yue and Y Chen, Comput. Math. Appl. 76, 831 (2018)

    Article  MathSciNet  Google Scholar 

  25. M Shahriari and J Manafian, Pramana – J. Phys. 93: 3 (2019)

    Article  ADS  Google Scholar 

  26. Y Kai, Pramana – J. Phys. 93: 46 (2019)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Y Tang and W Zai, Comput. Math. Appl. 70(10), 2432 (2015)

    Article  MathSciNet  Google Scholar 

  29. A M Wazwaz, Int. J. Comput. Math. 82(2), 235 (2005)

    Article  MathSciNet  Google Scholar 

  30. Z L Wang and X Q Liu, Pramana – J. Phys. 85, 3 (2015)

    Article  ADS  Google Scholar 

  31. K U-H Tariq and A R Seadawy, Pramana – J. Phys. 91: 68 (2018)

    Article  ADS  Google Scholar 

  32. C S Liu, Chin. Phys. 14, 1710 (2005)

    Article  Google Scholar 

  33. C S Liu, Chin. Phys. 16, 1832 (2007)

    Article  Google Scholar 

  34. C S Liu, Commun. Theor. Phys. 49, 153 (2008)

    Article  ADS  Google Scholar 

  35. C S Liu, Comput. Phys. Commun. 181, 317 (2010)

    Article  ADS  Google Scholar 

  36. X Wang and Y Liu, Pramana – J. Phys. 92(3): 31 (2019)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Northeast Petroleum University, Daqing, 163318, China

    Bin Li & Chun-Yan Wang

  2. Department of Mathematics, Center of Nonlinear Science, Northeast Petroleum University, Daqing, 163318, China

    Chun-Yan Wang

Authors
  1. Bin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun-Yan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, B., Wang, CY. Patterns of propagation of high-order nonlinear dispersion wave modelled by the generalised KP equation. Pramana - J Phys 94, 63 (2020). https://doi.org/10.1007/s12043-020-1938-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-020-1938-5

Keywords

PACS

Search

Navigation