Skip to main content
SpringerLink
Log in

Some applications of the (G′/G, 1/G)-expansion method to find new exact solutions of NLEEs

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

The double (\(G'/G\), \(1/G\))-expansion method is an influential, effective and well-suited method to examine closed form traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we extract abundant wave solutions to the (2+1)-dimensional typical breaking soliton equation and the (1+1)-dimensional classical Boussinesq equation through this method. The wave solutions are presented in terms of hyperbolic function, trigonometric function and rational function. By means of the wave transformation, the NLEEs are reduced to nonlinear ordinary differential equation (ODE) and then the nonlinear ODE is utilized to examine the necessary NLEE. The method can be considered as the generalization of the (\(G'/G\)-expansion method established by Wang et al. and it is shown that the suggested method is a powerful mathematical tool for investigating nonlinear evolution equations.

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

Similar content being viewed by others

References

  1. G.T. Liu, T.Y. Fan, Phys. Lett. A 345, 161 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  2. Z. Yan, Chaos, Solitons Fractals 18, 299 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  3. M.L. Wang, Phys. Lett. A 199, 169 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  4. E. Fan, H. Zhang, Phys. Lett. A 246, 403 (1998)

    Article  ADS  Google Scholar 

  5. E.G. Fan, Phys. Lett. A 277, 212 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. B. Kilic, M. Inc, Waves Random Complex Media 25, 245 (2015)

    Article  Google Scholar 

  7. A.M. Wazwaz, Chaos, Solitons Fractals 28, 1005 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  8. E.M.E. Zayed, H.A. Zedan, K.A. Gepreel, Appl. Anal. 83, 1101 (2004)

    Article  MathSciNet  Google Scholar 

  9. A. Bekir, A. Boz, Phys. Lett. A 372, 1619 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  10. J.H. He, X.H. Wu, Chaos, Solitons Fractals 30, 700 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  11. M.A. Akbar, N.H.M. Ali, Prog. Appl. Math. 1, 30 (2011)

    Google Scholar 

  12. A.R. Seadawy, Comput. Math. Appl. 62, 3741 (2011)

    Article  MathSciNet  Google Scholar 

  13. A.R. Seadawy, K.E. Rashidy, Math. Comp. Model. 57, 1371 (2013)

    Article  Google Scholar 

  14. A.R. Seadawy, Comput. Math. Appl. 67, 172 (2014)

    Article  MathSciNet  Google Scholar 

  15. A.R. Seadawy, Comput. Math. Appl. 70, 345 (2015)

    Article  MathSciNet  Google Scholar 

  16. A.R. Seadawy, Comput. Math. Appl. 71, 201 (2016)

    Article  MathSciNet  Google Scholar 

  17. M. Arshad, A.R. Seadawy, D. Lu, J. Wang, Results Phys. 6, 1136 (2016)

    Article  ADS  Google Scholar 

  18. A.R. Seadawy, O.H.E. Kalaawy, R.B. Aldenari, Appl. Math. Comput. 280, 57 (2016)

    MathSciNet  Google Scholar 

  19. E. Yomba, Chaos, Solitons Fractals 27, 187 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Inc, B. Kilic, Kuwait J. Sci. 43, 81 (2016)

    Google Scholar 

  21. F. Tchier, M. Inc, B. Kilic, A. Akgul, Optik 128, 218 (2017)

    Article  ADS  Google Scholar 

  22. E.S. Selima, A.R. Seadawy, X. Yao, Eur. Phys. J. Plus 131, 425 (2016)

    Article  Google Scholar 

  23. M. Inc, B. Kilic, Proc. Roman. Acad. A 16, 430 (2015)

    Google Scholar 

  24. X.Z. Li, M.L. Wang, Phys. Lett. A 361, 115 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  25. M.L. Wang, X.Z. Li, J.L. Zhang, Phys. Lett. A 363, 96 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  26. M.S. Hashemi, M. Inc, B. Kilic, A. Akgul, Waves Random Complex Media 26, 259 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  27. M. Inc, B. Kilic, D. Baleanu, Optik 127, 1056 (2016)

    Article  ADS  Google Scholar 

  28. Sirendareji, Phys. Lett. A 356, 124 (2006)

    Article  ADS  Google Scholar 

  29. Sirendaoreji, Phys. Lett. A 363, 440 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  30. B. Kilic, M. Inc, J. Electromagn. Waves Appl. 30, 871 (2016)

    Article  Google Scholar 

  31. J.Q. Mei, H.Q. Zhang, Chaos, Solitons Fractals 20, 771 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  32. M.A. Helal, A.R. Seadawy, Phys. Scr. 80, 350 (2009)

    Article  Google Scholar 

  33. A.R. Seadawy, Stat. Mech. Appl. Phys. A 455, 44 (2016)

    Article  MathSciNet  Google Scholar 

  34. Zhenya Yan, Chaos, Solitons Fractals 18, 299 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  35. M.L. Wang, X. Li, J. Zhang, Phys. Lett. A 372, 417 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  36. E.M.E. Zayed, J. Appl. Math. Comput. 30, 89 (2009)

    Article  MathSciNet  Google Scholar 

  37. E.M.E. Zayed, K.A. Gepreel, J. Math. Phys. 50, 013502 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  38. H. Zhang, Commun. Nonlinear Sci. Numer. Simul. 14, 3220 (2009)

    Article  ADS  Google Scholar 

  39. S. Zhang, L. Dong, J.-M. Ba, T.-N. Sun, Phys. Lett. A 373, 905 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  40. M.A. Akbar, N.H.M. Ali, E.M.E. Zayed, Commun. Theor. Phys. 57, 173 (2012)

    Article  ADS  Google Scholar 

  41. Y.B. Zhou, C. Li, Commun. Theor. Phys. 51, 664 (2009)

    Article  ADS  Google Scholar 

  42. A.R. Seadawy, Eur. Phys. J. Plus 132, 29 (2017)

    Article  Google Scholar 

  43. F. Calogero, A. Degasperis, Nouvo Cimento B 39, 1 (1977)

    Article  ADS  Google Scholar 

  44. H.O. Roshid, M.A. Rahman, Results Phys. 4, 150 (2014)

    Article  Google Scholar 

  45. M.A. Akbar, N.H.M. Ali, E.M.E. Zayed, Math. Prob. Eng. 2012, 459879 (2012)

    Article  Google Scholar 

  46. E.M.E. Zayed, Shoron Al-Joudi, Math. Prob. Eng. 2010, 768573 (2010)

    Article  Google Scholar 

  47. S. Guo, Y. Zhou, Appl. Math. Comput. 215, 3214 (2010)

    MathSciNet  Google Scholar 

  48. L.X. Li, E.Q. Li, M.L. Wang, Appl. Math. A J. Chin. Univ. 25, 454 (2010)

    Article  Google Scholar 

  49. E.M.E. Zayed, M.A.M. Abdelaziz, Math. Prob. Eng. 2012, 725061 (2012)

    Article  Google Scholar 

  50. E.M.E. Zayed, S.A. Hoda Ibrahim, M.A.M. Abdelaziz, J. Appl. Math. 2012, 560531 (2012)

    Article  Google Scholar 

  51. S. Demiray, O. Unsal, A. Bekir, Acta Phys. Pol. A 125, 1093 (2014)

    Article  Google Scholar 

  52. M.M. Miah, H.M.S. Ali, M.A. Akbar, Cogent Math. 3, 1277506 (2016)

    Article  Google Scholar 

  53. S. Demiry, O. Unsal, A. Bekir, J. Egypt. Math. Soc. 23, 78 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Southeast University, Dhaka, Bangladesh

    M. Mamun Miah

  2. National Institute of Textile Engineering and Research, Dhaka, Bangladesh

    H. M. Shahadat Ali

  3. Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

    M. Ali Akbar

  4. Department of Mathematics, Saint Xavier University, Chicago, USA

    Abdul Majid Wazwaz

Authors
  1. M. Mamun Miah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. M. Shahadat Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Ali Akbar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abdul Majid Wazwaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Ali Akbar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mamun Miah, M., Shahadat Ali, H.M., Ali Akbar, M. et al. Some applications of the (G′/G, 1/G)-expansion method to find new exact solutions of NLEEs. Eur. Phys. J. Plus 132, 252 (2017). https://doi.org/10.1140/epjp/i2017-11571-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11571-0

Search

Navigation