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

Rida Tassew Redi; Akalu Abriham Anulo

doi:doi:10.11648/j.mcs.20180301.14

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

Rida Tassew Redi, Akalu Abriham Anulo

Published in Mathematics and Computer Science (Volume 3, Issue 1)

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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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
Y1  - 2018/04/09
PY  - 2018
N1  - https://doi.org/10.11648/j.mcs.20180301.14
DO  - 10.11648/j.mcs.20180301.14
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 23
EP  - 45
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

Rida Tassew Redi

Department of Mathematics, Institute of Technology, Dire Dawa University, Dire Dawa, Ethiopia
Akalu Abriham Anulo

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

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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

Copy | Download

@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}
}

Copy | Download

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
Y1  - 2018/04/09
PY  - 2018
N1  - https://doi.org/10.11648/j.mcs.20180301.14
DO  - 10.11648/j.mcs.20180301.14
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 23
EP  - 45
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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