Skip to main content
Log in

Exact propagating multi-anti-kink soliton solutions of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We explore the shape changing and clevaging nature of anti-kink solutions of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. We achieved this by invoking the multiple exp-function method aided with symbolic computation which remains an indispensable tool to deal with computational algebraic systems.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Ma, W.X.: Diversity of exact solutions to a restricted Boiti–Leon–Pempinelli dispersive long-wave system. Phys. Lett. A 319, 325–333 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hu, H.C., Tong, B., Lou, S.Y.: Nonsingular positon and complexiton solutions for the coupled KdV system. Phys. Lett. A 351, 403–412 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Malfliet, W.: Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60, 650–654 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Parkes, E.J., Duffy, B.R.: An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations. Comput. Phys. Commun. 98, 288–296 (1996)

    Article  MATH  Google Scholar 

  5. Fan, E.G.: Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277, 212–218 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kavitha, L., Akila, N., Prabhu, A., Kuzmanovska-Barandovska, O., Gopi, D.: Exact solitary solutions of an inhomogeneous modified nonlinear Schrödinger equation with competing nonlinearities. Math. Comput. Model. 53, 1095–1110 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. He, J.H., Wu, X.H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30(3), 700–708 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Shin, B.C., Darvishi, M.T., Barati, A.: Some exact and new solutions of the Nizhnik–Novikov–Vesselov equation using the exp-function method. Comput. Math. Appl. 58(11/12), 2147–2151 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Darvishi, M.T., Khani, F.: A series solution of the foam drainage equation. Comput. Math. Appl. 58, 360–368 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Aziz, A., Khani, F., Darvishi, M.T.: Homotopy analysis method for variable thermal conductivity heat flux gage with edge contact resistance. Zeitschrift für Naturforschung A Phys. Sci. 65a(10), 771–776 (2010)

    Google Scholar 

  11. Khani, F., Darvishi, M.T., Gorla, R.S.R.: Analytical investigation for cooling turbine disks with a non-Newtonian viscoelastic fluid. Comput. Math. Appl. 61, 172–1738 (2011)

    Article  MathSciNet  Google Scholar 

  12. Dai, Z.D., Liu, J., Li, D.L.: Applications of HTA and EHTA to YTSF equation. Appl. Math. Comput. 207, 360–364 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Wang, C.-J., Dai, Z.-D., Mu, G., Lin, S.-Q.: New periodic solutions for new (2+1)-dimensional KDV equation. Commun. Theor. Phys. 52, 862–864 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zheng, C.-L., Qiang, J.-Y., Wang, S.-H.: Stamding, periodic and solitary waves in (1+1)-dimensional Caudry–Dodd–Gibson–Sawada–Kortera system. Commun. Theor. Phys. 54, 1054–1058 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  15. Darvishi, M.T., Najafi, M.: A modification of extended homoclinic test approach to solve the (3+1)-dimensional potential-YTSF equation. Chin. Phys. Lett. 28(4), article no. 040202, (2011)

  16. Najafi, M., Najafi, M., Darvishi, M.T.: New exact solutions to the (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation: Modification of extended homoclinic test approach, Chin. Phys. Lett., 29(4), article no. 040202, (2012)

  17. Sirendaoreji, : A new auxiliary equation and exact traveling wave solutions of nonlinear equations. Phys. Lett. A 356, 124–130 (2006)

    Article  MATH  Google Scholar 

  18. Ma, H.C., Yu, Y.D., Ge, D.J.: New exact traveling wave solutions for the modified form of Degasperis–Procesi equation. Appl. Math. Comput. 203, 792–798 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bhrawy, A.H., Abdelkawy, M.A., Biswas, A.: Cnodial and snodial wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method. Commun. Nonlinear Sci. Numer. Simul. 18(4), 915–925 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  20. Bhrawy, A.H., Biswas, A., Javidi, M., Ma, W.-X., Pinar, Z., Yildirim, A.: New solutions for (1+1)-dimensional and (2+1)-dimensional Kaup-Kupershmidt equations. RM 63(1–2), 675–686 (2013)

  21. Bhrawy, A.H., Abdelkawy, M.A., Kumar, S., Biswas, A.: Solitons and other solutions to Kadomtsev–Petviashvili equation of B-type. Rom. J. Phys. 58(7–8), 729–748 (2013)

    MathSciNet  Google Scholar 

  22. Bhrawy, A.H., Kumar, S., Triki, H., Yildirim, A., Biswas, A.: Solitons and other solutions to the (3+1)-dimensional extended Kadomtsev–Petviashvili equation with power low nonlinearity. Rom. Rep. Phys. 65(1), 27–62 (2013)

    Google Scholar 

  23. Triki, H., Kara, A.H., Bhrawy, A., Biswas, A.: Soliton solution and conservation law of Gear–Grimshaw model for shallow water waves. Acta Phys. Pol. A 125(5), 1099–1106 (2014)

    Article  Google Scholar 

  24. Bhrawy, A.H.: An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system. Appl. Math. Comput. 247, 30–46 (2014)

    Article  MathSciNet  Google Scholar 

  25. Triki, H., Mirzazadeh, M., Bhrawy, A.H., Razborova, P., Biswas, A.: Soliton and other solutions to long-wave interaction equation. Rom. J. Phys. 60(1–2), 72–86 (2015)

    Google Scholar 

  26. Yusufoglu, E.: New solitary solutions for the MBBM equations using Exp-function method. Phys. Lett. A 372, 442–446 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  27. Hirota, R.: The Direct Method in Soliton Theory. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  28. Zhang, Y., Ye, L.Y., Lv, Y.N., Zhao, H.G.: Periodic wave solutions of the Boussinesq equation. J. Phys. A Math. Gen. 40, 5539–5549 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  29. Ma, W.X., Zhou, R.G., Gao, L.: Exact one-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions. Mod. Phys. Lett. A 24, 1677–1688 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  30. Ma, W.X., Fan, E.G.: Linear superposition principle applying to Hirota bilinear equations. Comput. Math. Appl. 61, 950–959 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  31. Date, E., Jimbo, M., Miwa, T.: Method for generating discrete soliton equations. III. J. Phys. Soc. 52, 388–393 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  32. Hirota, R.: Discrete analogue of a generalized Toda equation. J. Phys. Soc. Jpn. 50, 3785–3791 (1981)

    Article  MathSciNet  Google Scholar 

  33. Miwa, T.: On Hirota difference equations. Proc. Jpn. Acad. A58, 9–12 (1982)

    Article  MathSciNet  Google Scholar 

  34. Zhang, H., Li, B., Chen, Y.: Full symmetry groups, Painlevé integrability and exact solutions of the nonisospectral BKP equation. Appl. Math. Comput. 217, 1555–1560 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  35. Ma, W.X., Huang, T.W., Zhang, Y.: A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr., 82 (2010) Art. no. 065003

Download references

Acknowledgments

L.K. gratefully acknowledges financial support from UGC, India, in the form of a Research Award, NBHM, India, in the form of a major research project, DAE-BRNS, India, in the form of a Young Scientist Research Award, and ICTP, Italy, for providing support under regular associateship scheme.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Najafi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Darvishi, M.T., Najafi, M., Arbabi, S. et al. Exact propagating multi-anti-kink soliton solutions of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. Nonlinear Dyn 83, 1453–1462 (2016). https://doi.org/10.1007/s11071-015-2417-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2417-2

Keywords

Mathematical Subject Classification

Navigation