SpringerLink
Log in

Lump solutions of a (3+1)-dimensional B-type KP equation and its dimensionally reduced equations

  • Published:
Analysis and Mathematical Physics Aims and scope Submit manuscript

Abstract

On the basis of bilinear equation of a (3+1)-dimensional B-type KP equation, we construct the lump-type solutions by symbolic computation. The (3+1)-dimensional B-type KP equation can be used to describe the propagation of nonlinear waves in fluid dynamics. The lump solutions of three dimensionally reduced (2+1)-dimensional B-type KP equation are derived. The sufficient and necessary conditions to guarantee the analyticity, positiveness and localization of lump solutions are discussed. Figures are presented to illustrate the energy distribution of these lump wave solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Singh, N., Stepanyants, Y.: Obliquely propagating skew KP lumps. Wave Motion 64, 92–102 (2016)

    Article  MathSciNet  Google Scholar 

  2. Satsuma, J., Ablowitz, M.J.: Two-dimensional lumps in nonlinear dispersive systems. J. Math. Phys. 20(7), 1496–1503 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gilson, C.R., Nimmo, J.J.C.: Lump solutions of the BKP equation. Phys. Lett. A 147(8), 472–476 (1990)

    Article  MathSciNet  Google Scholar 

  4. Imai, K.: Dromion and lump solutions of the Ishimori-I equation. Prog. Theor. Phys. 98(5), 1013–1023 (1997)

    Article  Google Scholar 

  5. Ma, W.X.: Lump solutions to the Kadomtsev–Petviashvili equation. Phys. Lett. A 379(36), 1975–1978 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lü, X., Ma, W.X.: Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dyn. 85(2), 1217–1222 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Yang, J.Y., Ma, W.X.: Lump solutions to the BKP equation by symbolic computation. Int. J. Mod. Phys. B 30, 1640028 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tang, Y.N., Tao, S.Q., Guan, Q.: Lump solitons and the interaction phenomena of them for two classes of nonlinear evolution equations. Comput. Math. Appl. 72(9), 2334–2342 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ma, W.X., Qin, Z.Y., Lü, X.: Lump solutions to dimensionally reduced p-gKP and p-gBKP equations. Nonlinear Dyn. 84(2), 923–931 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lü, X., Chen, S.T., Ma, W.X.: Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation. Nonlinear Dyn. 86(1), 523–534 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ma, W.X., Zhou, Y., Dougherty, R.: Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations. Int. J. Mod. Phys. B 30, 1640018 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ma, W.X.: Lump-type solutions to the (3+1)-dimensional jimbo-miwa equation. Int. J. Nonlinear Sci. Numer. Simul. 17(7–8), 355–359 (2016)

    MathSciNet  MATH  Google Scholar 

  13. Wazwaz, A.M.: Two forms of (3+1)-dimensional B-type Kadomtsev–Petviashvili equation: multiple soliton solutions. Phys. Scr. 86(3), 035007 (2012)

    Article  MATH  Google Scholar 

  14. Huang, Z.R., Tian, B., Zhen, H.L., Yan, J., Wang, Y.P., Sun, Y.: Bäcklund transformations and soliton solutions for a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics. Nonlinear Dyn. 80(1), 1–7 (2015)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 41474102.

Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Zhonglong Zhao & Bo Han

Authors
  1. Zhonglong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhonglong Zhao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Z., Han, B. Lump solutions of a (3+1)-dimensional B-type KP equation and its dimensionally reduced equations. Anal.Math.Phys. 9, 119–130 (2019). https://doi.org/10.1007/s13324-017-0185-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13324-017-0185-5

Keywords

Search

Navigation