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Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method

Received: 17 January 2018     Accepted: 16 February 2018     Published: 9 April 2018
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Abstract

In this article, the improved G'/G-expansion method has been implemented to generate travelling wave solutions, where G(ŋ) satisfies the second order nonlinear ordinary differential equation. To show the advantages of the method, the Simplified Modified Camassa Holm (SMCH) equation has been investigated. Nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation.

Published in Mathematics and Computer Science (Volume 3, Issue 1)
DOI 10.11648/j.mcs.20180301.14
Page(s) 23-45
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), 2018. Published by Science Publishing Group

Keywords

Improved G'/G-Expansion Method, The SMCH Equation, Traveling Wave Solutions, Nonlinear Evolution Equations

References
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Cite This Article
  • APA Style

    Rida Tassew Redi, Akalu Abriham Anulo. (2018). Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method. Mathematics and Computer Science, 3(1), 23-45. https://doi.org/10.11648/j.mcs.20180301.14

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    ACS Style

    Rida Tassew Redi; Akalu Abriham Anulo. Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method. Math. Comput. Sci. 2018, 3(1), 23-45. doi: 10.11648/j.mcs.20180301.14

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    AMA Style

    Rida Tassew Redi, Akalu Abriham Anulo. Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method. Math Comput Sci. 2018;3(1):23-45. doi: 10.11648/j.mcs.20180301.14

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  • @article{10.11648/j.mcs.20180301.14,
      author = {Rida Tassew Redi and Akalu Abriham Anulo},
      title = {Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method},
      journal = {Mathematics and Computer Science},
      volume = {3},
      number = {1},
      pages = {23-45},
      doi = {10.11648/j.mcs.20180301.14},
      url = {https://doi.org/10.11648/j.mcs.20180301.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20180301.14},
      abstract = {In this article, the improved G'/G-expansion method has been implemented to generate travelling wave solutions, where G(ŋ)  satisfies the second order nonlinear ordinary differential equation. To show the advantages of the method, the Simplified Modified Camassa Holm (SMCH) equation has been investigated. Nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method
    AU  - Rida Tassew Redi
    AU  - Akalu Abriham Anulo
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    DO  - 10.11648/j.mcs.20180301.14
    T2  - Mathematics and Computer Science
    JF  - Mathematics and Computer Science
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    PB  - Science Publishing Group
    SN  - 2575-6028
    UR  - https://doi.org/10.11648/j.mcs.20180301.14
    AB  - In this article, the improved G'/G-expansion method has been implemented to generate travelling wave solutions, where G(ŋ)  satisfies the second order nonlinear ordinary differential equation. To show the advantages of the method, the Simplified Modified Camassa Holm (SMCH) equation has been investigated. Nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, Institute of Technology, Dire Dawa University, Dire Dawa, Ethiopia

  • Department of Mathematics, Institute of Technology, Dire Dawa University, Dire Dawa, Ethiopia

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