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On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method

Received: 19 August 2015     Accepted: 7 November 2015     Published: 14 December 2015
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Abstract

In this study, we have applied the generalized kudryashov method to the symmetric regularized long wave equation for obtaining some new analytical solutions such as trigonometric function solution, exponential function solution, complexl function solution, hyperbolic function solution after giving the fundamental properties of method. Afterwards, we have observed that these analytical solutions are verified the symmetric regularized long wave equation by means of Wolfram Mathematica 9. Then, we have drawn two and three dimensional surfaces of analytical solutions. Finally, we have submitted a conclusion to literature.

Published in Mathematics Letters (Volume 1, Issue 2)
DOI 10.11648/j.ml.20150102.11
Page(s) 10-16
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

Keywords

Generalized Kudryashov Method, Symmetric Regularized Long Wave Equation, Exponential Function Solution, Complex Function Solution, Hyperbolic Function Solution, Trigonometric Function Solution

References
[1] G. K. Watugala, Sumudu Transform: A New Integral Transform to Solve Differantial Equations and Control Engineering Problems, International Journal of Mathematical Education in Science and Technology, 1993, 24, 35-43.
[2] Y. Pandir, New exact solutions of the generalized Zakharov–Kuznetsov modified equal-width equation, Pramana journal of physics, 2014, 82(6), 949–964.
[3] H. Bulut, H. M. Baskonus and F. B. M. Belgacem, The Analytical Solutions of Some Fractional Ordinary Differential Equations by Sumudu Transform Method, Abstract and Applied Analysis, 2013.
[4] A. M. Wazwaz, The tanh method: solitons and periodic solutions for Dodd-Bullough-Mikhailov and Tzitzeica- Dodd-Bullough equations, Chaos, Solitons and Fractals, 2005, 25, 55-56.
[5] C.S. Liu, A new trial equation method and its applications, Communications in Theoretical Physics,2006, 45(3), 395-397.
[6] C.S. Liu, Trial Equation Method to Nonlinear Evolution Equations with Rank Inhomogeneous: Mathematical Discussions and Its Applications, Communications in Theoretical Physics, 2006, 45(2), 219–223.
[7] H. Bulut, Y. Pandir, H. M. Baskonus, Symmetrical Hyperbolic Fibonacci Function Solutions of Generalized Fisher Equation with Fractional Order, AIP Conf. Proc.,2013, 1558, 1914 (2013).
[8] Y. Pandir, Y. Gurefe, U, Kadak, and E. Misirli, Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstract and Applied Analysis, vol.2012, Article ID 478531, 16 pages, 2012.
[9] Ryabov, P. N., Sinelshchikov, D. I., and Kochanov, M. B., Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations, Applied Mathematics and Computation, 218(7), 3965–3972, (2011).
[10] Kudryashov, N. A., One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 17(6), 2248–2253, (2012).
[11] Lee J., and Sakthivel, R., Exact travelling wave solutions for some important nonlinear physical models, Pramana—Journal of Physics, 80(5), 757–769, (2013).
[12] Demiray, S.T., Pandir, Y., and Bulut, H., Generalized Kudryashov Method for Time-Fractional Differential Equations, Abstract and Applied Analysis, 2014, 13 pages, (2014).
[13] J. Manafian and I. Zamanpour, Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods, Statistics, Optimization And Information Computing, 2, 47–55, 2014.
Cite This Article
  • APA Style

    Hasan Bulut, Haci Mehmet Baskonus, Eren Cüvelek. (2015). On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method. Mathematics Letters, 1(2), 10-16. https://doi.org/10.11648/j.ml.20150102.11

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    ACS Style

    Hasan Bulut; Haci Mehmet Baskonus; Eren Cüvelek. On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method. Math. Lett. 2015, 1(2), 10-16. doi: 10.11648/j.ml.20150102.11

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    AMA Style

    Hasan Bulut, Haci Mehmet Baskonus, Eren Cüvelek. On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method. Math Lett. 2015;1(2):10-16. doi: 10.11648/j.ml.20150102.11

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  • @article{10.11648/j.ml.20150102.11,
      author = {Hasan Bulut and Haci Mehmet Baskonus and Eren Cüvelek},
      title = {On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method},
      journal = {Mathematics Letters},
      volume = {1},
      number = {2},
      pages = {10-16},
      doi = {10.11648/j.ml.20150102.11},
      url = {https://doi.org/10.11648/j.ml.20150102.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20150102.11},
      abstract = {In this study, we have applied the generalized kudryashov method to the symmetric regularized long wave equation for obtaining some new analytical solutions such as trigonometric function solution, exponential function solution, complexl function solution, hyperbolic function solution after giving the fundamental properties of method. Afterwards, we have observed that these analytical solutions are verified the symmetric regularized long wave equation by means of Wolfram Mathematica 9. Then, we have drawn two and three dimensional surfaces of analytical solutions. Finally, we have submitted a conclusion to literature.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method
    AU  - Hasan Bulut
    AU  - Haci Mehmet Baskonus
    AU  - Eren Cüvelek
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    N1  - https://doi.org/10.11648/j.ml.20150102.11
    DO  - 10.11648/j.ml.20150102.11
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
    SP  - 10
    EP  - 16
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20150102.11
    AB  - In this study, we have applied the generalized kudryashov method to the symmetric regularized long wave equation for obtaining some new analytical solutions such as trigonometric function solution, exponential function solution, complexl function solution, hyperbolic function solution after giving the fundamental properties of method. Afterwards, we have observed that these analytical solutions are verified the symmetric regularized long wave equation by means of Wolfram Mathematica 9. Then, we have drawn two and three dimensional surfaces of analytical solutions. Finally, we have submitted a conclusion to literature.
    VL  - 1
    IS  - 2
    ER  - 

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

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

  • Department of Mathematics, Firat University, Elazig, Turkey

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