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Bilinear form, auto-Bäcklund transformations and kink solutions of a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid

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Abstract

Fluid mechanics has been linked to a wide range of disciplines, such as atmospheric science, oceanography and astrophysics. In this paper, we focus our attention on a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid. Through the Hirota method, we derive a bilinear form. We obtain an auto-Bäcklund transformation based on the truncated Painlev\(\acute{\textrm{e}}\) expansion and a bilinear Bäcklund transformation based on the bilinear form. With the variable coefficients \(\alpha (t)\), \(\beta (t)\), \(\gamma (y,t)\), \(\delta (t)\) and \(\mu (t)\) taken as certain constraints, one- and two-kink solutions are shown. Based on the one-kink solutions, we take \(\gamma (y,t)\) as the linear and trigonometric functions of y, and then give the ring-type and periodic-type one-kink waves, where t and y are the independent variables. According to the two-kink solutions, we obtain the parabolic-type, linear-type and periodic-type kink waves.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. H Triki and A M Wazwaz, Commun. Nonlinear Sci. Numer. Simulat. 19, 404 (2014)

    Article  ADS  Google Scholar 

  2. L Wang, Y T Gao and F H Qi, Ann. Phys. 327, 1974 (2012)

  3. S Boscolo and C Finot, Opt. Laser Technol. 131, 106439 (2020)

    Article  Google Scholar 

  4. A Moradi, Phys. Lett. A 391, 127103 (2021)

    Article  Google Scholar 

  5. S Kumar, Pramana – J. Phys. 95, 161 (2021)

  6. X Y Gao, Phys. Fluids 35, 127106 (2023)

  7. F Y Liu, Y T Gao, X Yu and C C Ding, Nonlinear Dyn. 108, 1599 (2022)

  8. F Y Liu and Y T Gao, Appl. Math. Lett. 132, 108094 (2022)

  9. X H Wu and Y T Gao, Appl. Math. Lett. 137, 108476 (2023)

  10. X H Wu, Y T Gao, X Yu, L Q Li and C C Ding, Nonlinear Dyn. 111, 5641 (2023)

  11. N Nirmala, M J Vedan and B V Baby, J. Math. Phys. 27, 2640 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  12. T Brugarino, J. Math. Phys. 30, 1013 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  13. S Boscarino and S Y Cho, Appl. Math. Lett. 123, 107488 (2022)

    Article  Google Scholar 

  14. C I Martin, Appl. Math. Lett. 124, 107690 (2022)

    Article  Google Scholar 

  15. Z Amjad, Eur. Phys. J. Plus 137, 1036 (2022)

    Article  Google Scholar 

  16. R Singh and A M Wazwaz, Eur. Phys. J. Plus 137, 63 (2022)

    Article  Google Scholar 

  17. C K Kuo and W X Ma, Wave Random Complex 32, 629 (2022)

    Article  ADS  Google Scholar 

  18. B Ghanbari and C K Kuo, Phys. Scr. 96, 045203 (2021)

    Article  ADS  Google Scholar 

  19. T S Moretlo, B Muatjetjeja and A R Adem, Iran. J. Sci. Technol. Trans. Sci. 45, 1037 (2021)

    Article  MathSciNet  Google Scholar 

  20. Y Feng and S Bilige, Nonlinear Dyn. 106, 879 (2021)

    Article  Google Scholar 

  21. Y Kodama and Y J Ablowitz, Stud. Appl. Math. 64, 225 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  22. C C Hu, B Tian, X Y Wu, Y Q Yuan and Z Du, Eur. Phys. J. Plus 133, 40 (2018)

    Article  Google Scholar 

  23. Y Zhang and J Pang, J. Appl. Math. 2019, 7172860 (2019)

    Article  Google Scholar 

  24. S Kumar and B Mohan, Phys. Scr. 96, 125255 (2021)

    Article  ADS  Google Scholar 

  25. R Hirota, Direct method in soliton theory (Springer, Berlin, 1980)

    Book  Google Scholar 

  26. R Hirota, Phys. Rev. Lett. 27, 1192 (1971)

    Article  ADS  Google Scholar 

  27. M Vlieg-Hulstman and W D Halford, Comput. Math. Appl. 29, 39 (1995)

    Article  MathSciNet  Google Scholar 

  28. J J Nimmo, Phys. Lett. A 99, 279 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  29. Y X Ma, B Tian, Q X Qu, C C Wei and X Zhao, Chin. J. Phys. 73, 600 (2021)

    Article  Google Scholar 

  30. Z Yan and S Lou, Appl. Math. Lett. 104, 106271 (2020)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant Nos 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, China) (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yu-Qi Chen, Bo Tian, Yuan Shen & Tian-Yu Zhou

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  1. Yu-Qi Chen
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  2. Bo Tian
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  3. Yuan Shen
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Correspondence to Bo Tian.

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Chen, YQ., Tian, B., Shen, Y. et al. Bilinear form, auto-Bäcklund transformations and kink solutions of a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid. Pramana - J Phys 98, 66 (2024). https://doi.org/10.1007/s12043-024-02740-3

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