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Semi-rational and periodic wave solutions for the (3+1)-dimensional Jimbo–Miwa equation

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Abstract

In this paper, higher-order periodic wave solution in determinant form is investigated via the Kadomtsev–Petviashvili hierarchy reduction for the \((3+1)\)-dimensional Jimbo–Miwa equation. We obtain the breather and periodic wave via such solution. The breather is periodic in space and localized in time, while amplitude of the periodic wave changes with the value of y. Besides, interaction between the breather and periodic wave shows a different characteristic in which amplitude of the periodic wave changes after the interaction. By taking the long wave limit to the periodic wave solution, we obtain the semi-rational solution, and then derive the rogue wave and kink-like soliton. Furthermore, we conclude that (1) rogue wave can be obtained with the limit on the breather; (2) kink-like soliton can be obtained with the limit on the periodic wave. Via the semi-rational solution, interactions between the rogue wave and breather, between the kink-like soliton and breather, are illustrated.

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References

  1. C.S. Gardner, J.M. Greene, M.D. Kruskal, R.M. Miura, Phys. Rev. Lett. 19, 1095 (1967)

    Article  ADS  Google Scholar 

  2. M.J. Ablowitz, P.A. Clarkson, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1991)

    Book  Google Scholar 

  3. H. Bailung, S.K. Sharma, Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011)

    Article  ADS  Google Scholar 

  4. G.F. Yu, Z.W. Xu, Phys. Rev. E 91, 062902 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  5. K.B. Dysthe, K. Trulsen, Phys. Scr. 1999, 48 (1999)

    Article  Google Scholar 

  6. C.Q. Dai, H.P. Zhu, Ann. Phys. 341, 142 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  9. B. Guo, L. Ling, Q.P. Liu, Phys. Rev. E 85, 026607 (2012)

    Article  ADS  Google Scholar 

  10. A. Chabchoub, N. Hoffmann, M. Onorato, N. Ahmediev, Phys. Rev. X 2, 011015 (2012)

    Google Scholar 

  11. D.J. Kedziora, A. Ankiewicz, N. Ahmediev, Phys. Rev. E 85, 066601 (2012)

    Article  ADS  Google Scholar 

  12. S.V. Manakov, V.E. Zakharov, Phys. Lett. A 63, 205 (1977)

    Article  ADS  Google Scholar 

  13. W.R. Sun, L. Wang, Proc. R. Soc. A 474, 20170276 (2018)

    Article  ADS  Google Scholar 

  14. M.A. Abdou, Nonlinear Dyn. 52, 1 (2008)

    Article  Google Scholar 

  15. Z.Z. Lan, B. Gao, M.J. Du, Chaos Solitons Fractals 111, 169 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  16. X.Y. Xie, G.Q. Meng, Nonlinear Dyn. 93, 779 (2018)

    Article  Google Scholar 

  17. Y. Ohta, J. Yang, Proc. R. Soc. A 468, 1716 (2012)

    Article  ADS  Google Scholar 

  18. B.F. Feng, J. Phys. A 47, 355203 (2014)

    Article  MathSciNet  Google Scholar 

  19. Y. Ohta, J. Yang, Phys. Rev. E 86, 036604 (2012)

    Article  ADS  Google Scholar 

  20. J. Rao, K. Porsezian, J. He, Chaos 27, 083115 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  21. J. Chen, Y. Chen, B.F. Feng, K. Maruno, J. Phys. Soc. Jpn. 84, 034002 (2015)

    Article  ADS  Google Scholar 

  22. B.B. Kadomtsev, V.I. Petviashvili, Sov. Phys. Doki. 15, 539 (1970)

    ADS  Google Scholar 

  23. M. Sato, North-Holland Math. Stud. 81, 259 (1983)

    Article  Google Scholar 

  24. M. Jimbo, T. Miwa, Publ. Res. Inst. Math. Sci. 19, 943 (1983)

    Article  MathSciNet  Google Scholar 

  25. X.Y. Tang, Z.F. Liang, Phys. Lett. A 351, 398 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  26. Z. Dai, Z. Li, Z. Liu, D. Li, Phys. A 384, 285 (2007)

    Article  Google Scholar 

  27. A.M. Wazwaz, Appl. Math. Comput. 203, 592 (2008)

    MathSciNet  Google Scholar 

  28. T. Özis, I. Aslan, Phys. Lett. A 372, 7011 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  29. Y. Tang, W.X. Ma, W. Xu, L. Gao, Appl. Math. Comput. 217, 8722 (2011)

    MathSciNet  Google Scholar 

  30. Y. Tang, J. Tu, W.X. Ma, Appl. Math. Comput. 218, 10050 (2012)

    MathSciNet  Google Scholar 

  31. Y. Zhang, L. Jin, Y. Kang, Appl. Math. Comput. 219, 2601 (2012)

    MathSciNet  Google Scholar 

  32. J.Y. Yang, W.X. Ma, Comput. Math. Appl. 73, 220 (2017)

    Article  MathSciNet  Google Scholar 

  33. W. Tian, Z. Dai, J. Xie, L. Hu, Z. Naturforsch. A 73, 43 (2017)

    Article  ADS  Google Scholar 

  34. X. Yong, X. Li, Y. Huang, Appl. Math. Lett. 86, 222 (2018)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  36. C. He, Y. Tang, J. Ma, Comput. Math. Appl. 76, 2141 (2018)

    Article  MathSciNet  Google Scholar 

  37. C. Chen, Y. Chen, B.F. Feng, K. Maruno, arXiv:1712.00945 (2017)

  38. W. Liu, A.M. Wazwaz, X. Zheng, Commun. Nonlinear Sci. Numer. Simul. 67, 480 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  39. M.J. Ablowitz, J. Satsuma, J. Math. Phys. 19, 2180 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  40. J. Satsuma, M.J. Ablowitz, J. Math. Phys. 20, 1496 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  41. R. Hirota, The Direct Method in Soliton Theory (Cambridge Univ. Press, Cambridge, 2004)

    Book  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant nos. 11771415 and 11371337, by the Fundamental Research Funds for the Central Universities of China under Grant no. WK3470000005.

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Authors and Affiliations

  1. Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100864, China

    Xiang Luo

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Xiang Luo

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  1. Xiang Luo
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Correspondence to Xiang Luo.

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Luo, X. Semi-rational and periodic wave solutions for the (3+1)-dimensional Jimbo–Miwa equation. Eur. Phys. J. Plus 135, 36 (2020). https://doi.org/10.1140/epjp/s13360-019-00008-z

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