Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics

S. M. Rayhanul Islam

doi:doi:10.11648/j.ajam.20150303.14

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Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics

S. M. Rayhanul Islam

Published in American Journal of Applied Mathematics (Volume 3, Issue 3)

Received: 6 April 2015 Accepted: 18 April 2015 Published: 29 April 2015

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Abstract

In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The proposed method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.ajam.20150303.14
Page(s)	100-105
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

Exp(-Φ(ξ))-Expansion Method, Benney-Luke Equation, Nonlinear Evolution Equations, Traveling Wave Solution

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APA Style

S. M. Rayhanul Islam. (2015). Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics. American Journal of Applied Mathematics, 3(3), 100-105. https://doi.org/10.11648/j.ajam.20150303.14

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ACS Style

S. M. Rayhanul Islam. Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics. Am. J. Appl. Math. 2015, 3(3), 100-105. doi: 10.11648/j.ajam.20150303.14

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AMA Style

S. M. Rayhanul Islam. Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics. Am J Appl Math. 2015;3(3):100-105. doi: 10.11648/j.ajam.20150303.14

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@article{10.11648/j.ajam.20150303.14,
  author = {S. M. Rayhanul Islam},
  title = {Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {100-105},
  doi = {10.11648/j.ajam.20150303.14},
  url = {https://doi.org/10.11648/j.ajam.20150303.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.14},
  abstract = {In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The proposed method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.},
 year = {2015}
}

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TY  - JOUR
T1  - Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics
AU  - S. M. Rayhanul Islam
Y1  - 2015/04/29
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.14
DO  - 10.11648/j.ajam.20150303.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 100
EP  - 105
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.14
AB  - In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The proposed method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.
VL  - 3
IS  - 3
ER  -

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Author Information

S. M. Rayhanul Islam

Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh

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APA Style

S. M. Rayhanul Islam. (2015). Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics. American Journal of Applied Mathematics, 3(3), 100-105. https://doi.org/10.11648/j.ajam.20150303.14

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ACS Style

S. M. Rayhanul Islam. Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics. Am. J. Appl. Math. 2015, 3(3), 100-105. doi: 10.11648/j.ajam.20150303.14

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AMA Style

S. M. Rayhanul Islam. Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics. Am J Appl Math. 2015;3(3):100-105. doi: 10.11648/j.ajam.20150303.14

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@article{10.11648/j.ajam.20150303.14,
  author = {S. M. Rayhanul Islam},
  title = {Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {100-105},
  doi = {10.11648/j.ajam.20150303.14},
  url = {https://doi.org/10.11648/j.ajam.20150303.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.14},
  abstract = {In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The proposed method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics
AU  - S. M. Rayhanul Islam
Y1  - 2015/04/29
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.14
DO  - 10.11648/j.ajam.20150303.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 100
EP  - 105
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.14
AB  - In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The proposed method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.
VL  - 3
IS  - 3
ER  -

Copy | Download