Advertisement

Pfaffian and rational solutions for a new form of the (3 + 1) -dimensional BKP equation in fluid dynamics

  • Li ChengEmail author
  • Yi Zhang
Regular Article

Abstract.

By using the fundamental Pfaffian identity, a Pfaffian formulation is established for a new form of the (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics. Generating functions for Pfaffian entries need to satisfy a linear system of partial differential equations involving the combined equations. The resulting solutions formulas provide us with a comprehensive approach to construct rational solutions, particularly lump-type solutions. Furthermore, a large class of lump-type solutions is also constructed by straightforward symbolic computations.

References

  1. 1.
    R. Hirota, Phys. Rev. Lett. 27, 1192 (1971)ADSCrossRefGoogle Scholar
  2. 2.
    N.C. Freeman, J.J.C. Nimmo, Phys. Lett. A 95, 1 (1983)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    J.J.C. Nimmo, N.C. Freeman, Phys. Lett. A 95, 4 (1983)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    W.X. Ma, A. Abdeljabbar, M.G. Asaad, Appl. Math. Comput. 217, 10016 (2011)MathSciNetGoogle Scholar
  5. 5.
    W.X. Ma, Y. You, Chaos Solitons Fractals 22, 395 (2004)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    L. Cheng, Y. Zhang, Nonlinear Dyn. 90, 355 (2017)CrossRefGoogle Scholar
  7. 7.
    M.G. Asaad, W.X. Ma, Appl. Math. Comput. 218, 5524 (2012)MathSciNetGoogle Scholar
  8. 8.
    W.X. Ma, T.C. Xia, Phys. Scr. 87, 055003 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    Y. Ohta, J.K. Yang, Phys. Rev. E 86, 036604 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Ohta, J.K. Yang, Proc. R. Soc. A 468, 1716 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Ohta, J.K. Yang, J. Phys. A 46, 105202 (2013)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    W.X. Ma, Phys. Lett. A 301, 35 (2002)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    R. Hirota, J. Phys. Soc. Jpn. 58, 2285 (1989)ADSCrossRefGoogle Scholar
  14. 14.
    C.R. Gilson, J.J.C. Nimmo, Phys. Lett. A 147, 472 (1990)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    W.X. Ma, Y. Zhang, Y.N. Tang, J.Y. Tu, Appl. Math. Comput. 218, 7174 (2012)MathSciNetGoogle Scholar
  16. 16.
    A.M. Wazwaz, Phys. Scr. 86, 035007 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    X.Y. Gao, Ocean Eng. 96, 245 (2015)CrossRefGoogle Scholar
  18. 18.
    E.R. Caianiello, Combinatorics and Renormalization in Quantum Field Theory (Benjamin, London, 1973)Google Scholar
  19. 19.
    R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press, Cambridge, 2004)Google Scholar
  20. 20.
    M.J. Ablowitz, S. Chakravarty, A.D. Trubatch, J. Villarroel, Phys. Lett. A 267, 132 (2000)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    W.X. Ma, Y. Zhou, R. Dougherty, Int. J. Mod. Phys. B 30, 1640018 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    W.X. Ma, Int. J. Nonlinear Sci. Numer. 17, 355 (2016)CrossRefGoogle Scholar
  23. 23.
    H. Gao, W.G. Cheng, T.Z. Xu, G.W. Wang, Eur. Phys. J. Plus 133, 116 (2018)CrossRefGoogle Scholar
  24. 24.
    C.C. Hu, B. Tian, X.Y. Wu, Y.Q. Yuan, Z. Du, Eur. Phys. J. Plus 133, 40 (2018)CrossRefGoogle Scholar
  25. 25.
    X. Lü, W.X. Ma, Nonlinear Dyn. 85, 1217 (2016)CrossRefGoogle Scholar
  26. 26.
    X. Lü, W.X. Ma, Y. Zhou, C.M. Khalique, Comput. Math. Appl. 71, 1560 (2016)MathSciNetCrossRefGoogle Scholar
  27. 27.
    L. Cheng, Y. Zhang, Mod. Phys. Lett. B 31, 1750224 (2017)ADSCrossRefGoogle Scholar
  28. 28.
    J. Satsuma, M.J. Ablowitz, J. Math. Phys. 20, 1496 (1979)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    X.M. Zhu, D.J. Zhang, D.Y. Chen, Commun. Theor. Phys. 55, 13 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    A.S. Fokas, D.E. Pelinovsky, C. Sulem, Physica D 152-153, 189 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    V.G. Dubrovsky, I.B. Formusatik, Phys. Lett. A 313, 68 (2003)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    W.X. Ma, Phys. Lett. A 379, 1975 (2015)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    W.X. Ma, E.G. Fan, Comput. Math. Appl. 61, 950 (2011)MathSciNetCrossRefGoogle Scholar
  34. 34.
    H.C. Zheng, W.X. Ma, X. Gu, Appl. Math. Comput. 220, 226 (2013)MathSciNetGoogle Scholar
  35. 35.
    Y. Zhou, W.X. Ma, Comput. Math. Appl. 73, 1697 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Normal SchoolJinhua PolytechnicJinhuaChina
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaChina

Personalised recommendations