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The envelope travelling wave solutions to the Gerdjikov–Ivanov model

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Abstract

In this paper, by using the complete discrimination system of the polynomial method, the classification of the envelope travelling wave solutions to the Gerdjikov–Ivanov model is obtained. The complete result shows that there exist rich patterns of travelling wave solutions to the Gerdjikov–Ivanov model, including solitary solutions, periodic solutions, rational singular solutions and double periodic continuous and non-continuous solutions. Among those, some new solutions are given.

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References

  1. E-G Fan, Integrable systems and computer algebra (Academic Press, Beijing, China, 2004)

    Google Scholar 

  2. R Hirota, The direct method in soliton theory (Cambridge University Press, 2004)

    Book  MATH  Google Scholar 

  3. C-S Liu, Chaos Solitons Fractals 42(1), 441 (2009)

    Article  ADS  Google Scholar 

  4. C-S Liu, Rep. Math. Phys. 67(1), 109 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  5. A M Wazwaz, Partial differential equations and solitary waves theory (Springer Science and Business Media, 2010)

    Google Scholar 

  6. J Yang, Nonlinear waves in integrable and nonintegrable systems (Society for Industrial and Applied Mathematics, Philadelphia, 2010)

    Book  MATH  Google Scholar 

  7. S T R Rizvi, K Ali, A Sardar, M Younis and A Bekir, Pramana – J. Phys. 88(1): 16 (2017)

    Article  ADS  Google Scholar 

  8. C-S Liu, Commun. Theor. Phys. 44(5), 799 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  9. C-S Liu, Commun. Theor. Phys. 54(6), 991 (2006)

    ADS  Google Scholar 

  10. C-S Liu, Commun. Theor. Phys. 43(4), 787 (2005)

    ADS  Google Scholar 

  11. C-S Liu, Commun. Theor. Phys. 48(4), 601 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  12. C-S Liu, Chin. Phys. Lett. 21(12), 2369 (2004)

    Article  ADS  Google Scholar 

  13. C-S Liu, Commun. Theor. Phys. 49(2), 291 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  14. C-S Liu, Commun. Theor. Phys. 49(1), 153 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  15. C-S Liu, Comput. Phys. Commun. 181(2), 317 (2010)

    Article  ADS  Google Scholar 

  16. C-S Liu, Acta Phys. Sin. 54(6), 2505 (2005)

    Google Scholar 

  17. C-S Liu, Acta Phys. Sin. 54(10), 4506 (2005)

    Google Scholar 

  18. C-S Liu, Commun. Theor. Phys. 45(2), 219 (2006)

    Article  ADS  Google Scholar 

  19. C-S Liu, Commun. Theor. Phys. 54, 3395 (2006)

    Google Scholar 

  20. C-S Liu, Found. Phys. 41(5), 793 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  21. C-S Liu, Chaos Soliton Fractals 40, 708 (2009)

    Article  ADS  Google Scholar 

  22. S Yang, Mod. Phys. Lett. B 24(3), 363 (2010)

    Article  Google Scholar 

  23. S Yang, Z. Naturf. A 73(1), 1 (2018)

    Article  ADS  Google Scholar 

  24. H L Fan and X Li, Pramana – J. Phys. 81(6), 925 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  25. D Dai and Y Yuan, Appl. Math. Comput. 242, 729 (2014)

    MathSciNet  Google Scholar 

  26. Y Kai, Pramana – J. Phys. 87(4): 59 (2016)

    Article  ADS  Google Scholar 

  27. H L Fan, Appl. Math. Comput. 219(2), 748 (2012)

    MathSciNet  Google Scholar 

  28. C Y Wang, J Guan and B Y Wang, Pramana – J. Phys. 77(4), 759 (2011)

    Article  ADS  Google Scholar 

  29. Y Liu, Appl. Math. Comput. 217(12), 5866 (2011)

    MathSciNet  Google Scholar 

  30. Y Cheng, Comput. Math. Appl. 62(10), 3987 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  31. Y Pandir, Y Gurefe and E Misirli, Phys. Scr. 87(2), 025003 (2013)

    Article  ADS  Google Scholar 

  32. Y Pandir, Pramana – J. Phys. 82(6), 949 (2014)

    Article  ADS  Google Scholar 

  33. H Bulut, Y Pandir and H M Baskonus, AIP Conf. Proc. 1558(1), 1914 (2013)

    Article  ADS  Google Scholar 

  34. S Tuluce Demiray and H Bulut, Waves Random Complex Media 25(1), 75 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  35. H Bulut, Y Pandir and S Tuluce Demiray, Waves Random Complex Media 24(4), 439 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  36. V S Gerdjikov and M I Ivanov, Bulg. J. Phys. 10, 130 (1983)

    Google Scholar 

  37. A Kundu, Physica D 25, 399 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  38. E G Fan, J. Phys. A 33, 6925 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  39. X Lü, W X Ma, J Yu and F Lin, Nonlinear Dyn. 82, 1211 (2015)

    Article  Google Scholar 

  40. J Manafian and M Lakestani, Optik – Int. J. Light Electron Opt. 127(20), 9603 (2016)

    Article  Google Scholar 

  41. N Kadkhoda and H Jafari, Optik – Int. J. Light Electron Opt. 139, 72 (2017)

    Article  Google Scholar 

  42. E Mjølhus, J. Plasma Phys. 16, 321 (1976)

    Article  ADS  Google Scholar 

  43. G S’anchez-Arriaga, J R Sanmartin and S A Elaskar, Phys. Plasmas 14, 082108 (2007)

    Article  ADS  Google Scholar 

  44. G S’anchez-Arriaga, Phys. Plasmas 17, 082313 (2010)

    Article  ADS  Google Scholar 

  45. N Tzoar and M Jain, Phys. Rev. A 23, 1266 (1981)

    Article  ADS  Google Scholar 

  46. D Anderson and M Lisak, Phys. Rev. A 27, 1393 (1983)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The author would like to thank the reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of ATM, Civil Aviation Flight University of China, Guanghan,  618307, People’s Republic of China

    Shu Yang

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  1. Shu Yang
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Correspondence to Shu Yang.

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Yang, S. The envelope travelling wave solutions to the Gerdjikov–Ivanov model. Pramana - J Phys 91, 36 (2018). https://doi.org/10.1007/s12043-018-1618-x

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  • DOI: https://doi.org/10.1007/s12043-018-1618-x

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