Advertisement

Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics

  • Cong-Cong Hu
  • Bo TianEmail author
  • Xiao-Yu Wu
  • Yu-Qiang Yuan
  • Zhong Du
Regular Article

Abstract.

Under investigation is a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a fluid. Via the Hirota method and symbolic computation, we obtain the mixed lump-kink and mixed rogue wave-kink solutions. Through the mixed lump-kink solutions, we observe three different phenomena between a lump and one kink. For the fusion phenomenon, a lump and a kink are merged with the lump’s energy transferring into the kink gradually, until the lump merges into the kink completely. Fission phenomenon displays that a lump separates from a kink. The last phenomenon shows that a lump travels together with a kink with their amplitudes unchanged. In addition, we graphically study the interaction between a rogue wave and a pair of the kinks. It can be observed that the rogue wave arises from one kink and disappears into the other kink. At certain time, the amplitude of the rogue wave reaches the maximum.

References

  1. 1.
    R. Guo, Y.F. Liu, H.Q. Hao, Nonlinear Dyn. 80, 1221 (2015)CrossRefGoogle Scholar
  2. 2.
    N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373, 675 (2009)CrossRefADSGoogle Scholar
  3. 3.
    H. Bailung, S.K. Sharma, Y. Nakamura, Phys. Rev. Lett. 107, 814 (2011)CrossRefGoogle Scholar
  4. 4.
    H.X. Jia, Y.J. Liu, Y.N. Wang, Z. Naturforsch. A 27, 71 (2015)Google Scholar
  5. 5.
    D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)CrossRefADSGoogle Scholar
  6. 6.
    L. Stenflo, M. Marklund, J. Plasma Phys. 76, 293 (2010)CrossRefADSGoogle Scholar
  7. 7.
    Z.Y. Qin, G. Mu, Phys. Rev. E 86, 036601 (2012)CrossRefADSGoogle Scholar
  8. 8.
    Z.Y. Yan, Commun. Theor. Phys. 54, 947 (2010)CrossRefADSGoogle Scholar
  9. 9.
    D.H. Peregrine, J. Aust. Math. Soc. Ser. B Appl. Math. 25, 16 (1983)MathSciNetCrossRefGoogle Scholar
  10. 10.
    R. Guo, H.H. Zhao, Y.A. Wang, Nonlinear Dyn. 83, 2475 (2016)CrossRefGoogle Scholar
  11. 11.
    D.W. Zuo, Y.T. Gao, L. Xue, Y.J. Feng, Opt. Quantum Electron. 48, 1 (2016)CrossRefGoogle Scholar
  12. 12.
    H.C. Ma, A.P. Deng, Commun. Theor. Phys. 65, 546 (2016)CrossRefADSGoogle Scholar
  13. 13.
    E. Falcon, C. Laroche, S. Fauve, Phys. Rev. Lett. 89, 204501 (2002)CrossRefADSGoogle Scholar
  14. 14.
    H.Q. Zhang, W.X. Ma, Nonlinear Dyn. 87, 2305 (2016)CrossRefGoogle Scholar
  15. 15.
    V.I. Petviashvili, O.V. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere (Energoatomizdat, Moscow, 1989)Google Scholar
  16. 16.
    D.E. Pelinovsky, Y.A. Stepanyants, Y.S. Kivshar, Phys. Rev. E 51, 5016 (1995)MathSciNetCrossRefADSGoogle Scholar
  17. 17.
    W.X. Ma, Phys. Lett. A 379, 1975 (2015)MathSciNetCrossRefADSGoogle Scholar
  18. 18.
    X. Lü, S.T. Chen, W.X. Ma, Nonlinear Dyn. 86, 523 (2016)CrossRefGoogle Scholar
  19. 19.
    C.J. Wang, Nonlinear Dyn. 84, 697 (2016)CrossRefGoogle Scholar
  20. 20.
    J.B. Zhang, W.X. Ma, Comput. Math. Appl. 74, 591 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    N.Y. Tang, S.Q. Tao, Q. Guan, Comput. Math. Appl. 72, 2334 (2016)MathSciNetCrossRefGoogle Scholar
  22. 22.
    T.C. Kofane, M. Fokou, A. Mohamadou, E. Yomba, Eur. Phys. J. Plus 132, 465 (2017)CrossRefGoogle Scholar
  23. 23.
    X.E. Zhang, Y. Chen, Commun. Nonlinear Sci. Numer. Simul. 52, 24 (2017)MathSciNetCrossRefADSGoogle Scholar
  24. 24.
    X.Y. Gao, Appl. Math. Lett. 73, 143 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    T.T. Jia, Y.Z. Chai, H.Q. Hao, Superlattice Microstruct. 105, 172 (2017)CrossRefADSGoogle Scholar
  26. 26.
    T.T. Jia, Y.Z. Chai, H.Q. Hao, Math. Probl. Eng. 2016, 11 (2016)Google Scholar
  27. 27.
    J.J. Su, Y.T. Gao, S.L. Jia, Commun. Nonlinear Sci. Numer. Simul. 50, 128 (2017)MathSciNetCrossRefADSGoogle Scholar
  28. 28.
    J.J. Su, Y.T. Gao, Superlattice Microstruct. 104, 498 (2017)CrossRefADSGoogle Scholar
  29. 29.
    G.F. Deng, Y.T. Gao, Superlattice Microstruct. 109, 345 (2017)CrossRefGoogle Scholar
  30. 30.
    B.B. Kadomtsev, V.I. Petviashvili, Sov. Phys. Dokl. 15, 539 (1970)ADSGoogle Scholar
  31. 31.
    M.J. Ablowitz, H. Segur, J. Fluid Mech. 92, 691 (1979)MathSciNetCrossRefADSGoogle Scholar
  32. 32.
    T. Xu, F.W. Sun, Y. Zhang, J. Li, Comput. Math. Math. Phys. 54, 97 (2014)MathSciNetCrossRefGoogle Scholar
  33. 33.
    G.F. Deng, Y.T. Gao, Eur. Phys. J. Plus 132, 255 (2017)CrossRefGoogle Scholar
  34. 34.
    M. Abudiab, C.M. Khalique, Adv. Differ. Equ. 2013, 221 (2013)CrossRefGoogle Scholar
  35. 35.
    Z.Z. Lan, Y.T. Gao, J.W. Yang, C.Q. Su, C. Zhao, Z. Gao, Appl. Math. Lett. 60, 96 (2016)MathSciNetCrossRefGoogle Scholar
  36. 36.
    W.Q. Hu, Y.T. Gao, S.L. Jia, Q.M. Huang, Z.Z. Lan, Eur. Phys. J. Plus 131, 390 (2016)CrossRefGoogle Scholar
  37. 37.
    Q.M. Huang, Y.T. Gao, S.L. Jia, Y.L. Wang, G.F. Deng, Nonlinear Dyn. 87, 2529 (2017)CrossRefGoogle Scholar
  38. 38.
    Q.M. Huang, Y.T. Gao, Nonlinear Dyn. 89, 2855 (2017)CrossRefGoogle Scholar
  39. 39.
    A.H. Bhrawy, M.A. Abdelkawy, S. Kumar, A. Biswas, Rom. J. Phys. 58, 729 (2013)Google Scholar
  40. 40.
    X.Y. Gao, Ocean Eng. 96, 245 (2015)CrossRefGoogle Scholar
  41. 41.
    N. Liu, Nonlinear Dyn. 82, 311 (2015)CrossRefGoogle Scholar
  42. 42.
    Z.H. Xu, H.L. Chen, Z.D. Dai, Pramana - J. Phys. 87, 31 (2016)CrossRefADSGoogle Scholar
  43. 43.
    X.B. Wang, S.F. Tian, L.L. Feng, H. Yan, T.T. Zhang, Nonlinear Dyn. 88, 2265 (2017)CrossRefGoogle Scholar
  44. 44.
    L. Cheng, Y. Zhang, Commun. Theor. Phys. 68, 1 (2017)CrossRefGoogle Scholar
  45. 45.
    M.T. Darvishi, M. Najafi, S. Arbabi, L. Kavitha, Nonlinear Dyn. 83, 1453 (2016)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina

Personalised recommendations