Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method

Ayrin Aktar; Md Mashiur Rahhman; Kamalesh Chandra Roy

doi:doi:10.11648/j.ajam.20190702.12

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Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method

Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy

Published in American Journal of Applied Mathematics (Volume 7, Issue 2)

Received: 21 April 2019 Accepted: 13 June 2019 Published: 27 June 2019

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Abstract

This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.

Published in	American Journal of Applied Mathematics (Volume 7, Issue 2)
DOI	10.11648/j.ajam.20190702.12
Page(s)	49-57
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), 2019. Published by Science Publishing Group

Keywords

Novel Exponential Expansion Method, Boussinesq Equation, Solitary Wave Solutions, Periodic Solutions

References

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APA Style

Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy. (2019). Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. American Journal of Applied Mathematics, 7(2), 49-57. https://doi.org/10.11648/j.ajam.20190702.12

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ACS Style

Ayrin Aktar; Md Mashiur Rahhman; Kamalesh Chandra Roy. Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. Am. J. Appl. Math. 2019, 7(2), 49-57. doi: 10.11648/j.ajam.20190702.12

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AMA Style

Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy. Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. Am J Appl Math. 2019;7(2):49-57. doi: 10.11648/j.ajam.20190702.12

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@article{10.11648/j.ajam.20190702.12,
  author = {Ayrin Aktar and Md Mashiur Rahhman and Kamalesh Chandra Roy},
  title = {Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {2},
  pages = {49-57},
  doi = {10.11648/j.ajam.20190702.12},
  url = {https://doi.org/10.11648/j.ajam.20190702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190702.12},
  abstract = {This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.},
 year = {2019}
}

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TY  - JOUR
T1  - Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method
AU  - Ayrin Aktar
AU  - Md Mashiur Rahhman
AU  - Kamalesh Chandra Roy
Y1  - 2019/06/27
PY  - 2019
N1  - https://doi.org/10.11648/j.ajam.20190702.12
DO  - 10.11648/j.ajam.20190702.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 49
EP  - 57
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20190702.12
AB  - This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.
VL  - 7
IS  - 2
ER  -

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Author Information

Ayrin Aktar

Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
Md Mashiur Rahhman

Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
Kamalesh Chandra Roy

Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh

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APA Style

Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy. (2019). Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. American Journal of Applied Mathematics, 7(2), 49-57. https://doi.org/10.11648/j.ajam.20190702.12

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ACS Style

Ayrin Aktar; Md Mashiur Rahhman; Kamalesh Chandra Roy. Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. Am. J. Appl. Math. 2019, 7(2), 49-57. doi: 10.11648/j.ajam.20190702.12

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AMA Style

Ayrin Aktar, Md Mashiur Rahhman, Kamalesh Chandra Roy. Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method. Am J Appl Math. 2019;7(2):49-57. doi: 10.11648/j.ajam.20190702.12

Copy | Download

@article{10.11648/j.ajam.20190702.12,
  author = {Ayrin Aktar and Md Mashiur Rahhman and Kamalesh Chandra Roy},
  title = {Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {2},
  pages = {49-57},
  doi = {10.11648/j.ajam.20190702.12},
  url = {https://doi.org/10.11648/j.ajam.20190702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190702.12},
  abstract = {This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method
AU  - Ayrin Aktar
AU  - Md Mashiur Rahhman
AU  - Kamalesh Chandra Roy
Y1  - 2019/06/27
PY  - 2019
N1  - https://doi.org/10.11648/j.ajam.20190702.12
DO  - 10.11648/j.ajam.20190702.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 49
EP  - 57
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20190702.12
AB  - This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.
VL  - 7
IS  - 2
ER  -

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