Skip to main content
SpringerLink
Log in

Elliptic function soliton solutions of the higher-order nonlinear dispersive Kundu–Eckhaus dynamical equation with applications and stability

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

Abstract

In this paper, we employ the four mathematical methods, namely improved simple equation method (SEM), modified extended SEM, generalized exp\((-\Phi (\xi ))\)-expansion technique and modified extended mapping technique, and attain exact solutions in various forms of Kundu–Eckhaus (K–E) equation. The wave solutions in the forms of bright and dark solitons, periodic solitary wave, kink and anti-kink soliton, trigonometric and hyperbolic trigonometric function and rational function are achieved. The movements of few results are presented graphically, which are useful to mathematician and physician for understanding the complex phenomena. The standard linear stability analysis is employed to examine the stability of the equation. This shows that exact solutions are stable. The results obtained are novel in nature and have good potential application values. The results demonstrate that these techniques are simple, effective and more powerful to solve 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. D Bleecker and G Csordas Basic Partial Differential Equations (New York: Chapman and Hall) (1995)

    MATH  Google Scholar 

  2. L Lam Nonlinear Physics for Beginners (Singapore: World Scientific) (1998)

    Book  Google Scholar 

  3. M Arshad, A R Seadawy, D Lu and J Wang Optik 157 597 (2018)

  4. J D Logan An Introduction to Nonlinear Partial Differential Equations (New York: John Wiley) (1994)

    MATH  Google Scholar 

  5. A Seadawy, M Arshad and D Lu Eur. Phys. J. Plus 132 1 (2017)

  6. M Arshad, A R Seadawy and D Lu Superlattices Microstruct. 112 422 (2017)

  7. J M Soto-Crespo, N Devine, N P Hoffmann and N Akhmediev Phys. Rev. E 90 032902 (2014)

    Article  ADS  Google Scholar 

  8. M S Abdel Latif Appl. Math. Comput. 247 501 (2014)

  9. X Wang, B Yang, Y Chen and Y Yang Phys. Scr. 89 095210 (2014)

    Article  ADS  Google Scholar 

  10. D Lu, A Seadawy, M Arshad and J Wang Resul. Phys. 7 899 (2017)

  11. K Ul-Haq Tariq and A Seadawy Resul. Phys. 7 1143 (2017)

    Article  ADS  Google Scholar 

  12. A R Seadawy, M Arshad and D Lu Eur. Phys. J. Plus 132 (2017)

  13. D Lu, A R Seadawy and M Arshad Optik 140 136 (2017)

    Article  ADS  Google Scholar 

  14. A Seadawy Eur. Phys. J. Plus 132 1 (2017)

    Google Scholar 

  15. N Nasreen, D Lu and M Arshad Optik 161 221 (2018)

    Article  ADS  Google Scholar 

  16. A R Seadawy Phys. A 439 124 (2015)

    Article  MathSciNet  Google Scholar 

  17. A R Seadawy Int. J. Comput. Methods 15 1850017 (2018)

    Article  MathSciNet  Google Scholar 

  18. A R Seadawy and K El-Rashidy Pramana J. Phys. 87 20 (2016)

  19. A H Khater, D K Callebaut, M A Helal and A R Seadawy Phys. Script. 74 384 (2006)

    Article  ADS  Google Scholar 

  20. M Arshad, A R Seadawy and D Lu Optik 138 40 (2017)

    Article  ADS  Google Scholar 

  21. M A Helal and A R Seadawy Comput. Math. Appl. 64 3557 (2012)

    Article  MathSciNet  Google Scholar 

  22. D Levi and C Scimiterna J. Phys. A 42 465203 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. P Wang, B Tian, K Sun and F H Qi Appl. Math. Comput. 251 233 (2015)

    MathSciNet  Google Scholar 

  24. M Arshad, A Seadawy and D Lu J. Electromagn. Waves Appl. 31 1711 (2017)

    Article  Google Scholar 

  25. I Ahmed, A R Seadawy and D Lu Phys. Script. 94 (2019)

  26. R S Johnson Proc. R. Soc. Lond. A 357 131 (1977)

  27. Y Kodama J. Stat. Phys. 39 597 (1985)

    Article  ADS  Google Scholar 

  28. P A Clarkson and J A Tuszynski J. Phys. A 23 4269 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  29. H M Baskonusa and H Bulut Waves Random Complex Media 25 417 (2015)

  30. D Lu, A Seadawy, J Wang, M Arshad and U Farooq Pramana-J. Phys. (2019) (Accepted)

  31. N Taghizadeh, M Mirzazadeh and F Tascan Appl. Math. Lett. 25 798 (2012)

    Article  MathSciNet  Google Scholar 

  32. X Y Gao J. Math. Phys. 56 014101 (2015)

  33. M Eslami, M Mirzazadeh, B F Tascan and A Biswas Optik 125 3107 (2014)

    Article  ADS  Google Scholar 

  34. X Y Gao Ocean Eng. 96 245 (2015)

    Article  Google Scholar 

  35. W R Sun, B Tian, Y Jiang and H L Zhen Phys. Rev. E 91 02320 (2015)

    Google Scholar 

  36. H L Zhen, B Tian, Y F Wang and D Y Liu Phys. Plasmas 22 03230 (2015)

    Google Scholar 

  37. Y F Wang, B Tian, M Wang and H L Zhen Nonlinear Dyn. 79 721 (2015)

    Article  Google Scholar 

  38. W Yu, Q Zhou, M Mirzazadeh, W Liu and A Biswas J. Adv. Res 15 69 (2019)

    Article  Google Scholar 

  39. M Mirzazadeh, Y Yildirim, E Yasar, H Triki, Q Zhou, S P Moshokoa, M Z Ullah, A R Seadawy, A Biswas and M Belic Optik - Int. J. Light Electron Opt. 154 551 (2018)

    Article  Google Scholar 

  40. M Mirzazadeh, M Eslami and A Biswas Comput. Appl. Math. 33 831 (2014)

    Article  MathSciNet  Google Scholar 

  41. M Eslami and M Mirzazadeh Nonlinear Dyn. 83 731 (2016)

    Article  Google Scholar 

  42. W Liu, Y Zhang, H Triki, M Mirzazadeh, M Ekici, Q Zhou, A Biswas and M Belic Nonlinear Dyn. 95 557 (2019)

    Article  Google Scholar 

  43. W Yu, M Ekici, M Mirzazadeh, Q Zhou and W Liu Optik 165 341 (2018)

    Article  ADS  Google Scholar 

  44. Z-J Yang, S-M Zhang, X-L Li and Z-G Pang Appl. Math. Lett. 82 64 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  45. R-R Jia and R Guo Appl. Math. Lett. 93 117 (2019)

    Article  MathSciNet  Google Scholar 

  46. G P Agrawal Nonlinear Fiber Optics, 5th edn. New York (2013)

  47. M Saha and A K Sarma Commun. Nonlinear Sci. Numer. Simul. 18 2420 (2013)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the China Post-doctoral science foundation, Peoples Republic of China (PRC) (Grant No. 2019M651715).

Author information

Authors and Affiliations

  1. Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Dianchen Lu & Muhammad Arshad

  2. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

  3. Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Aly R. Seadawy

Authors
  1. Dianchen Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aly R. Seadawy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Arshad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aly R. Seadawy.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, D., Seadawy, A.R. & Arshad, M. Elliptic function soliton solutions of the higher-order nonlinear dispersive Kundu–Eckhaus dynamical equation with applications and stability. Indian J Phys 95, 691–704 (2021). https://doi.org/10.1007/s12648-019-01629-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-019-01629-x

Keywords

PACS Nos.

Search

Navigation