Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models

M. Mashiur Rahhman; Ayrin Aktar; Kamalesh Chandra Roy

doi:doi:10.11648/j.ajam.20180605.11

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Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models

M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy

Published in American Journal of Applied Mathematics (Volume 6, Issue 5)

Received: 4 October 2018 Accepted: 7 November 2018 Published: 18 December 2018

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Abstract

The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.

Published in	American Journal of Applied Mathematics (Volume 6, Issue 5)
DOI	10.11648/j.ajam.20180605.11
Page(s)	149-158
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

Coupled Classical Boussinesq Equation, Boussinesq-Kadomtsev-Petviashili Equation, Solitary Wave Solution, Periodic Wave Solution

References

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APA Style

M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy. (2018). Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. American Journal of Applied Mathematics, 6(5), 149-158. https://doi.org/10.11648/j.ajam.20180605.11

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ACS Style

M. Mashiur Rahhman; Ayrin Aktar; Kamalesh Chandra Roy. Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. Am. J. Appl. Math. 2018, 6(5), 149-158. doi: 10.11648/j.ajam.20180605.11

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AMA Style

M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy. Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. Am J Appl Math. 2018;6(5):149-158. doi: 10.11648/j.ajam.20180605.11

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@article{10.11648/j.ajam.20180605.11,
  author = {M. Mashiur Rahhman and Ayrin Aktar and Kamalesh Chandra Roy},
  title = {Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models},
  journal = {American Journal of Applied Mathematics},
  volume = {6},
  number = {5},
  pages = {149-158},
  doi = {10.11648/j.ajam.20180605.11},
  url = {https://doi.org/10.11648/j.ajam.20180605.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180605.11},
  abstract = {The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.},
 year = {2018}
}

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TY  - JOUR
T1  - Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models
AU  - M. Mashiur Rahhman
AU  - Ayrin Aktar
AU  - Kamalesh Chandra Roy
Y1  - 2018/12/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20180605.11
DO  - 10.11648/j.ajam.20180605.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 149
EP  - 158
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20180605.11
AB  - The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.
VL  - 6
IS  - 5
ER  -

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Author Information

M. Mashiur Rahhman

Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
Ayrin Aktar

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

Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh

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Plain Text BibTeX RIS

APA Style

M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy. (2018). Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. American Journal of Applied Mathematics, 6(5), 149-158. https://doi.org/10.11648/j.ajam.20180605.11

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ACS Style

M. Mashiur Rahhman; Ayrin Aktar; Kamalesh Chandra Roy. Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. Am. J. Appl. Math. 2018, 6(5), 149-158. doi: 10.11648/j.ajam.20180605.11

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AMA Style

M. Mashiur Rahhman, Ayrin Aktar, Kamalesh Chandra Roy. Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models. Am J Appl Math. 2018;6(5):149-158. doi: 10.11648/j.ajam.20180605.11

Copy | Download

@article{10.11648/j.ajam.20180605.11,
  author = {M. Mashiur Rahhman and Ayrin Aktar and Kamalesh Chandra Roy},
  title = {Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models},
  journal = {American Journal of Applied Mathematics},
  volume = {6},
  number = {5},
  pages = {149-158},
  doi = {10.11648/j.ajam.20180605.11},
  url = {https://doi.org/10.11648/j.ajam.20180605.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180605.11},
  abstract = {The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models
AU  - M. Mashiur Rahhman
AU  - Ayrin Aktar
AU  - Kamalesh Chandra Roy
Y1  - 2018/12/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20180605.11
DO  - 10.11648/j.ajam.20180605.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 149
EP  - 158
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20180605.11
AB  - The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.
VL  - 6
IS  - 5
ER  -

Copy | Download