Skip to main content
SpringerLink
Log in

New solitary wave solutions to the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff and the Kadomtsev–Petviashvili hierarchy equations

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

In this paper, with the help of Wolfram Mathematica 9 we employ the powerful sine-Gordon expansion method in investigating the solution structures of the two well known nonlinear evolution equations, namely; Calogero–Bogoyavlenskii–Schiff and Kadomtsev–Petviashvili hierarchy equations. We obtain new solutions with complex, hyperbolic and trigonometric function structures. All the obtained solutions in this paper verified their corresponding equations. We also plot the three- and two-dimensional graphics of all the obtained solutions in this paper by using the same program in Wolfram Mathematica 9. We finally submit a comprehensive conclusion.

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

Access this article

Log in via an institution

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
Fig. 5

Similar content being viewed by others

References

  1. A R Seadawy and A Sayed Abstr. Appl. Anal. 2014 7 (2014)

    Article  Google Scholar 

  2. R Arora and A Kumar Appl. Math. 1(2) 59 (2011)

    Article  Google Scholar 

  3. W Jia, L Biao and Y Wang-Chuan Chin. Phys. B 19(3) 7 (2010)

    Article  Google Scholar 

  4. Y Li and D Li Appl. Math. Sci. 6(12) 579 (2012)

    MathSciNet  Google Scholar 

  5. J Cao, M Song and J Zhou Int. J. Math. Anal. 6(43) 2141 (2012)

    Google Scholar 

  6. M F Aghdaei and J Manafianheris J. Math. Ext. 5(2) 91 (2011)

    MathSciNet  Google Scholar 

  7. M J Ablowitz, B Prinari and A D Trubatch Dyn. PDE 1(3) 239 (2004)

    Google Scholar 

  8. A Neamaty, B Agheli and R Darzi J. Nonlinear Evol. Equ. Appl. 2015(6) 91 (2016)

    Google Scholar 

  9. H Bulut and H M Baskonus Math. Comput. Appl. 21(2) 6 (2016)

    Google Scholar 

  10. M Postolache, Y Gurefe, A Sonmezoglu, M Ekici and E Misirli U.P.B. Sci. Bull. Ser. A 76(2) 10 (2014)

    Google Scholar 

  11. B I Ita and P Tchoua Res. J. Phys. Sci. 1(1) 21 (2013)

    Google Scholar 

  12. Y Keskin and G Oturanc Math. Comput. Appl. 15(3) 382 (2010)

    MathSciNet  Google Scholar 

  13. M A Abdou, A Hendi and B Aaid Stud. Nonlinear Sci. 3(1) 14 (2012)

    Google Scholar 

  14. M A Noor, K I Noor, A Waheed and E A Al-Said Comput. Math. Appl. 62 2126 (2011)

    Article  MathSciNet  Google Scholar 

  15. S A El-Wakil, M A Madkour, M T Attia, A Elhanbaly and M A Abdou Int. J. Nonlinear Sci. 7(1) 12 (2009)

    MathSciNet  Google Scholar 

  16. A S Alofi Int. Math. Forum 7(53) 2639 (2012)

    MathSciNet  Google Scholar 

  17. E Hesameddini and F Fotros Int. Math. Forum 7(21) 1047 (2012)

    MathSciNet  Google Scholar 

  18. S S Ray Int. J. Nonlinear Sci. 4(3) 227 (2007)

    MathSciNet  Google Scholar 

  19. E Yusufoglu and A Bekir Math. Comput. Model. 48 1694 (2008)

    Article  Google Scholar 

  20. E M E Zayed and S A H Ibrahim Chin. Phys. Lett. 29(6) 4 (2012)

    Article  Google Scholar 

  21. K Khan, M A Akbar and S M R Islam SpringerPlus 3(724) 8 (2014)

    Google Scholar 

  22. Z Zhang, J Zhong, S S Dou, J Liu, D Peng and T Gao Rom. Rep. Phys. 65(4) 1155 (2013)

    Google Scholar 

  23. A Jabbari and H Kheiri Int. J. Nonlinear Sci. 12(3) 291 (2011)

    MathSciNet  Google Scholar 

  24. A A Soliman and M A Abdou J. Comput. Appl. Math. 207 111 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  25. A M Wazwaz Proc. Rom. Acad. 16(1) 32 (2015)

    MathSciNet  Google Scholar 

  26. H Or-Roshid, M A Akbar, M Nur-Alam, M F Hoque and N Rahman SpringerPlus 3(122) 6 (2014)

    Google Scholar 

  27. N Kadkhoda Casp. J. Math. Sci. 4(2) 189 (2015)

    MathSciNet  Google Scholar 

  28. H M Baskonus, H Bulut and F B M Belgacem J. Comput. Appl. Math. 312 257 (2017)

    Article  MathSciNet  Google Scholar 

  29. H M Baskonus and H Bulut Waves Random Complex Media 25(4) 720 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  30. H M Baskonus and H Bulut Waves Random Complex Media 26(4) 613 (2016)

    Article  MathSciNet  Google Scholar 

  31. M Eslami Comput. Methods Differ. Equ. 2(2) 115 (2014)

    MathSciNet  Google Scholar 

  32. M A Abdelkawy, M A Alghamdi and AH Bhrawy Sci. Res. Essays 7(27) 2417 (2012)

    Article  Google Scholar 

  33. K M Owolabi and A Atangana J. Comput. Nonlinear Dyn. 12(3) 031010 (2016)

    Article  Google Scholar 

  34. A Atangana Eur. Phys. J. Plus 131(10) 373 (2016)

    Article  Google Scholar 

  35. B S T Alkahtani and A Atangana Chaos Solitons Fractals 89 566 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  36. A Atangana and R T Alqahtani J. Comput. Theor. Nanosci. 13(5) 2710 (2016)

    Article  Google Scholar 

  37. B S T Alkahtani and A Atangana Open Phys. 14 (1) 106 (2016)

    Article  Google Scholar 

  38. M Kaplan A Bekir and A Akbulut Nonlinear Dyn. 85(4) 2843 (2016)

    Article  Google Scholar 

  39. K A Gepreel Comput. Math. Appl. 72(9) 2072 (2016)

    Article  MathSciNet  Google Scholar 

  40. C Yan Phys. Lett. A 22(4) 77 (1996)

    Article  ADS  Google Scholar 

  41. Z Yan and H Zhang Phys. Lett. A 252 291 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  42. Y Zhen-Ya, Z Hong-oing and F En-Gui Acta Phys. Sin. 48(1) 1 (1999)

    Google Scholar 

  43. M Hong-Cai, Q Zhen-Yun and D Ai-Ping Acta Phys. Sin. 59(2) 141 (2013)

    Google Scholar 

  44. E M E Zayed and A G Al-Nowehy Zeitschrift fur Naturforschung A 70(9) 775 (2015)

    Google Scholar 

  45. H M Baskonus, H Bulut and A Atangana Smart Mater. Struct. 25(3) 035022 (2016)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Munzur University, Tunceli, Turkey

    Haci Mehmet Baskonus

  2. Department of Mathematics, Firat University, Elazig, Turkey

    Tukur Abdulkadir Sulaiman & Hasan Bulut

Authors
  1. Haci Mehmet Baskonus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tukur Abdulkadir Sulaiman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hasan Bulut
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haci Mehmet Baskonus.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baskonus, H.M., Sulaiman, T.A. & Bulut, H. New solitary wave solutions to the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff and the Kadomtsev–Petviashvili hierarchy equations. Indian J Phys 91, 1237–1243 (2017). https://doi.org/10.1007/s12648-017-1033-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-017-1033-z

Keywords

PACS Nos.

Search

Navigation