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Multiple rogue wave solutions of a generalised Hietarinta-type equation

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Abstract

In this paper, multiple rogue wave solutions of a generalised Hietarinta-type fourth-order equation in (\(2+1\))-dimensional dispersive waves were studied by applying the bilinear method. We obtained its 1-rogue wave, 3-rogue wave and 6-rogue wave solutions. Similarly, their corresponding maps which can finely explain their physical structure and properties were graphically shown through symbolic computation approach. It is obvious that the centre of the 3-rogue wave possesses a triangular structure while 6-rogue wave has a hexagon structure and they are made of three and six independent 1-rogue waves, respectively. Furthermore, the results obtained have immensely augmented the exact solutions of the generalised Hietarinta-type equation on the available literature and enabled us to understand the nonlinear dynamic system deeply.

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References

  1. Y X Geng and J B Li, Appl. Math. Comput. 203, 536 (2008)

    MathSciNet  Google Scholar 

  2. S T Chen and W X Ma, Complexity 2019, 8787460 (2019)

    Google Scholar 

  3. J G Liu, M X You, L Zhou and J P Ai, Z. Angew. Math. Phys. 70, 4 (2019)

    Google Scholar 

  4. X Lü, W X Ma, J Yu and C M Khalique, Commun. Nonlinear Sci. Numer. Simul. 31, 40 (2016)

    Article  MathSciNet  Google Scholar 

  5. A M Wazwaz, Appl. Math. Lett. 64, 21 (2017)

    Article  MathSciNet  Google Scholar 

  6. C R Zhang, B Tian, X Q Qu, L Liu and H Y Tian, Z. Angew. Math. Phys. 71, 18 (2020)

    Google Scholar 

  7. R F Zhang and S D Bilige, Mod. Phys. Lett. B 33, 06 (2019)

    Google Scholar 

  8. Y Q Yuan, B Tian, Q X Qu, X H Zhao and X X Du, Z. Angew. Math. Phys. 71, 46 (2020)

    Google Scholar 

  9. J G Liu and H Yan, Nonlinear Dyn. 90, 363 (2017)

    Article  Google Scholar 

  10. H H Dong and Y F Zhang, Commun. Theor. Phys. 63, 401 (2015)

    Article  ADS  Google Scholar 

  11. Y Z Li and J G Liu, Nonlinear Dyn. 91, 497 (2018)

    Article  Google Scholar 

  12. Z L Zhao and Y F Zhang, Math. Meth. Appl. Sci. 38, 4262 (2015)

    Article  Google Scholar 

  13. X E Zhang, Y Chen and Y Zhang, Comput. Math. Appl. 74, 2341 (2017)

    Article  MathSciNet  Google Scholar 

  14. H X Xu, Z Y Yang, L C Zhao, L Duan and W L Yang, Phys. Lett. A 382, 1738 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  15. X Lü, W X Ma, Y Zhou and C M Khalique, Comput. Math. Appl. 71, 1560 (2016)

    Article  MathSciNet  Google Scholar 

  16. Y Zhang, H H Dong, X E Zhang and H W Yang, Comput. Math. Appl. 73, 246 (2017)

    Article  MathSciNet  Google Scholar 

  17. X M Wang and S D Bilige, Commun. Theor. Phys. 72, 04500 (2020)

    Google Scholar 

  18. X Lü, W X Ma, S T Chen and C M Khalique, Appl. Math. Lett. 58, 13 (2016)

    Article  MathSciNet  Google Scholar 

  19. M S Osman and A M Wazwaz, Appl. Math.Comput. 321, 282 (2018)

    MathSciNet  Google Scholar 

  20. J G Liu, Appl. Math. Lett. 86, 36 (2018)

    Article  MathSciNet  Google Scholar 

  21. W X Ma and Y Zhou, J. Diff. Eq. 264, 2633 (2018)

    Article  ADS  Google Scholar 

  22. T Fang and Y H Wang, Comput. Math. Appl. 76, 1476 (2018)

    Article  MathSciNet  Google Scholar 

  23. Y Y Feng, S D Bilige and X M Wang, Phys. Scr. 95, 095201 (2020)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  25. H Q Zhang and W X Ma, Nonlinear Dyn. 87(4), 2305 (2017)

    Article  Google Scholar 

  26. J Q Lü, S D Bilige and T M Chaolu, Nonlinear Dyn. 91(2), 1669 (2018)

    Article  Google Scholar 

  27. J Q Lü and S D Bilige, Nonlinear Dyn. 90, 2119 (2017)

    Article  Google Scholar 

  28. W X Ma and Y Zhou, J. Diff. Eq. 264(4), 2633 (2018)

    Article  ADS  Google Scholar 

  29. W X Ma, Nonlinear Dyn. 85, 1217 (2016)

    Article  Google Scholar 

  30. W X Ma, Int. J. Nonlinear Sci. Numer. Simul. 22, (2021), https://doi.org/10.1515/ijnsns-2020-0214

  31. W X Ma, Opt. Quant. Electron. 52, 511 (2020)

    Article  Google Scholar 

  32. W X Ma, Y Zhang and Y N Tang, East Asian J. Appl. Math. 10, 732 (2020)

    Google Scholar 

  33. J Y Yang, W X Ma and C M Khalique, The Eur. Phys. J. Plus 135, 494 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  35. Z S Lü and Y N Chen, Solitons Fractals 81, 218 (2015)

    Article  ADS  Google Scholar 

  36. X Y Wen and H T Wang, Appl. Math. Lett. 111, 106683 (2021)

  37. R M Li and X G Geng, Commun. Nonlinear Sci. Numer. Simul. 90, 105408 (2020)

    Article  MathSciNet  Google Scholar 

  38. Y Jiang and Q X Qu, Math. Comput. Simul. 179, 57 (2021)

    Article  Google Scholar 

  39. A Maccar, Phys. Lett. A 384, 126740 (2020)

    Article  MathSciNet  Google Scholar 

  40. W H Liu and Y F Zhang, Z. Angew. Math. Phys. 70(4), 112 (2019)

    Google Scholar 

  41. Q L Zha, Comput. Math. Appl. 75(9), 3331 (2018)

    Article  MathSciNet  Google Scholar 

  42. S Batwa and W X Ma, Front. Math. China 15, 435450 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (12061054, 11661060), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-20-A06), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (2018LH01013) and Program for Graduate Research Innovation of Inner Mongolia Autonomous Region (SZ2020063).

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Authors and Affiliations

  1. Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, People’s Republic of China

    Yueyang Feng & Sudao Bilige

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  1. Yueyang Feng
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  2. Sudao Bilige
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Correspondence to Sudao Bilige.

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Feng, Y., Bilige, S. Multiple rogue wave solutions of a generalised Hietarinta-type equation. Pramana - J Phys 95, 151 (2021). https://doi.org/10.1007/s12043-021-02166-1

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