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Modified extended exp-function method for a system of nonlinear partial differential equations defined by seismic sea waves

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Abstract

Nonlinear partial differential equations are the main area of focus for researchers and scientists doing research in applied mathematics. Finding solutions of these nonlinear partial differential equations had gained considerable importance over the last few decades. In this work, an analytical technique named extended exp-function method is introduced for finding archetype exact solutions of innovative nonlinear coupled Konno–Oono equation. Different types of travelling wave solutions, i.e. complex hyperbolic function and complex trigonometric function solutions, with numerous capricious parameters are revealed. Subsequently, by using Maple 16, we plot 2D and 3D surfaces of analytical solutions obtained in this article. The depiction of the technique is straight, useful and can be applied to other nonlinear systems of partial differential equations.

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References

  1. K Chunga and T Toulkeridis, J. Tsunami Soc. Int. 33, 55 (2014)

    Google Scholar 

  2. E Yusufoğlu, Phys. Lett. A 372, 442 (2008)

    Article  ADS  Google Scholar 

  3. E M E Zayed and S Al-Joudi, Math. Probl. Eng. 2010, 19 (2010), https://doi.org/10.1155/2010/768573

    Article  Google Scholar 

  4. H Jafari, H Tajadodi and D Baleanu, J. Comput. Nonlinear Dyn. 9(2), 021019 (2014), https://doi.org/10.1115/1.4025770

    Article  Google Scholar 

  5. B Zheng, Sci. World J.  2013, (2013), Article ID 465723, https://doi.org/10.1155/2013/465723

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

    Article  MathSciNet  ADS  Google Scholar 

  7. X H Wu and J H He, Comput. Math. Appl. 54, 966 (2007)

    Article  MathSciNet  Google Scholar 

  8. F Özpinar, H M Baskonus and H Bulut, Entropy 17, 8267 (2015), https://doi.org/10.3390/e17127878

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  10. M G Hafez, M N Alam and M A Akbar, World Appl. Sci. J. 32(10), 2150 (2014), https://doi.org/10.5829/idosi.wasj.2014.32.10.3569

    Google Scholar 

  11. M Shakeel, Q M Ul-Hassan, J Ahmad and S T Mohyud-Din, Adv. Math. Phys. 2014, (2014), Article ID 181594

  12. K Khan and M A Akbar, Math. Phys. 2013, (2013), Article ID 685736

  13. L Guan, X Geng and Z Li, R. Swed. Acad. Sci. 89(7), 075210 (2014)

    Google Scholar 

  14. M E Sabbagh, A Shehata and A Saleh, Int. J. Pure Appl. Math. 101(2), 171 (2015)

    Google Scholar 

  15. A Ali, M A Iqbal and S T Mohyud-Din, Pramana–J. Phys. 87: 79 (2016), https://doi.org/10.1007/s12043-016-1277-8

    Article  ADS  Google Scholar 

  16. K Ayub, M Y Khan, Q M-Hassan and J Ahmad, Pramana – J. Phys. 89: 45 (2017), https://doi.org/10.1007/s12043-017-1447-3

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif, Pakistan

    Muhammad Shakeel

  2. Faculty of Sciences, HITEC University, Taxila, Pakistan

    Syed Tauseef Mohyud-Din

  3. Department of Mathematics, Faculty of Basic and Applied Sciences, The University of Poonch, Rawalakot, Pakistan

    Muhammad Asad Iqbal

Authors
  1. Muhammad Shakeel
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  2. Syed Tauseef Mohyud-Din
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  3. Muhammad Asad Iqbal
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Correspondence to Syed Tauseef Mohyud-Din.

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Shakeel, M., Mohyud-Din, S.T. & Iqbal, M.A. Modified extended exp-function method for a system of nonlinear partial differential equations defined by seismic sea waves. Pramana - J Phys 91, 28 (2018). https://doi.org/10.1007/s12043-018-1601-6

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  • DOI: https://doi.org/10.1007/s12043-018-1601-6

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