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Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method

Received: 6 June 2015     Accepted: 18 June 2015     Published: 19 June 2015
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Abstract

In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.

Published in Mathematics Letters (Volume 1, Issue 1)
DOI 10.11648/j.ml.20150101.11
Page(s) 1-9
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

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Keywords

The Bernoulli Sub-Equation Function Method, Nonlinear Partial Vakhnenko-Parkes Differential Equation, The Reduced Ostrovsky Equation, Rational Function Solution, Exponential Function Solution, Hyperbolic Function Solution, Complex Trigonometric Function Solution

References
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Cite This Article
  • APA Style

    Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir. (2015). Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Mathematics Letters, 1(1), 1-9. https://doi.org/10.11648/j.ml.20150101.11

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    ACS Style

    Haci Mehmet Baskonus; Hasan Bulut; Dilara Gizem Emir. Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Math. Lett. 2015, 1(1), 1-9. doi: 10.11648/j.ml.20150101.11

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    AMA Style

    Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir. Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Math Lett. 2015;1(1):1-9. doi: 10.11648/j.ml.20150101.11

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  • @article{10.11648/j.ml.20150101.11,
      author = {Haci Mehmet Baskonus and Hasan Bulut and Dilara Gizem Emir},
      title = {Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method},
      journal = {Mathematics Letters},
      volume = {1},
      number = {1},
      pages = {1-9},
      doi = {10.11648/j.ml.20150101.11},
      url = {https://doi.org/10.11648/j.ml.20150101.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20150101.11},
      abstract = {In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.},
     year = {2015}
    }
    

    Copy | Download

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    T1  - Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method
    AU  - Haci Mehmet Baskonus
    AU  - Hasan Bulut
    AU  - Dilara Gizem Emir
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    N1  - https://doi.org/10.11648/j.ml.20150101.11
    DO  - 10.11648/j.ml.20150101.11
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
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    EP  - 9
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20150101.11
    AB  - In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.
    VL  - 1
    IS  - 1
    ER  - 

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Author Information
  • Department of Computer Engineering, Tunceli University, Tunceli, Turkey

  • Department of Mathematics, University of Firat, Elazig, Turkey

  • Department of Mathematics, University of Firat, Elazig, Turkey

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