Solving Nonlinear Evolution Equations by <i>(G'/G)</i>-Expansion Method

Attia Rani; Munazza Saeed; Muhammad Ashraf; Rakshanda Zaman; Qazi Mahmood-Ul-Hassan; Kamran Ayub; Muhammad Yaqub Khan; Madiha Afzal

doi:doi:10.11648/j.optics.20180701.17

Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method

Attia Rani, Munazza Saeed, Muhammad Ashraf, Rakshanda Zaman, Qazi Mahmood-Ul-Hassan, Kamran Ayub, Muhammad Yaqub Khan, Madiha Afzal

Published in Optics (Volume 7, Issue 1)

Received: 24 June 2018 Accepted: 13 July 2018 Published: 8 August 2018

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Abstract

Nonlinear mathematical models and their solutions attain much attention in soliton theory. In this paper, main focus is to find travelling wave solutions of foam drainage equation and NLEE of fourth order. (G'/G)-expansion method is applied on these nonlinear differential equations. Wave transformation is used to convert nonlinear partial differential equation into an ordinary differential equation. It is observed that (G'/G)-expansion method is advanced and easy tool for finding solution of NLEEs in engineering, optics and mathematical physics. The proposed method is highly effective and reliable.

Published in	Optics (Volume 7, Issue 1)
DOI	10.11648/j.optics.20180701.17
Page(s)	43-53
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), 2024. Published by Science Publishing Group

Keywords

(G'/G)-Expansion Method, Nonlinear Evolution Equations, Travelling Wave Solutions, Maple 18

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APA Style

Attia Rani, Munazza Saeed, Muhammad Ashraf, Rakshanda Zaman, Qazi Mahmood-Ul-Hassan, et al. (2018). Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method. Optics, 7(1), 43-53. https://doi.org/10.11648/j.optics.20180701.17

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ACS Style

Attia Rani; Munazza Saeed; Muhammad Ashraf; Rakshanda Zaman; Qazi Mahmood-Ul-Hassan, et al. Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method. Optics. 2018, 7(1), 43-53. doi: 10.11648/j.optics.20180701.17

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AMA Style

Attia Rani, Munazza Saeed, Muhammad Ashraf, Rakshanda Zaman, Qazi Mahmood-Ul-Hassan, et al. Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method. Optics. 2018;7(1):43-53. doi: 10.11648/j.optics.20180701.17

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@article{10.11648/j.optics.20180701.17,
  author = {Attia Rani and Munazza Saeed and Muhammad Ashraf and Rakshanda Zaman and Qazi Mahmood-Ul-Hassan and Kamran Ayub and Muhammad Yaqub Khan and Madiha Afzal},
  title = {Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method},
  journal = {Optics},
  volume = {7},
  number = {1},
  pages = {43-53},
  doi = {10.11648/j.optics.20180701.17},
  url = {https://doi.org/10.11648/j.optics.20180701.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.optics.20180701.17},
  abstract = {Nonlinear mathematical models and their solutions attain much attention in soliton theory. In this paper, main focus is to find travelling wave solutions of foam drainage equation and NLEE of fourth order. (G'/G)-expansion method is applied on these nonlinear differential equations. Wave transformation is used to convert nonlinear partial differential equation into an ordinary differential equation. It is observed that (G'/G)-expansion method is advanced and easy tool for finding solution of NLEEs in engineering, optics and mathematical physics. The proposed method is highly effective and reliable.},
 year = {2018}
}

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TY  - JOUR
T1  - Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method
AU  - Attia Rani
AU  - Munazza Saeed
AU  - Muhammad Ashraf
AU  - Rakshanda Zaman
AU  - Qazi Mahmood-Ul-Hassan
AU  - Kamran Ayub
AU  - Muhammad Yaqub Khan
AU  - Madiha Afzal
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.optics.20180701.17
DO  - 10.11648/j.optics.20180701.17
T2  - Optics
JF  - Optics
JO  - Optics
SP  - 43
EP  - 53
PB  - Science Publishing Group
SN  - 2328-7810
UR  - https://doi.org/10.11648/j.optics.20180701.17
AB  - Nonlinear mathematical models and their solutions attain much attention in soliton theory. In this paper, main focus is to find travelling wave solutions of foam drainage equation and NLEE of fourth order. (G'/G)-expansion method is applied on these nonlinear differential equations. Wave transformation is used to convert nonlinear partial differential equation into an ordinary differential equation. It is observed that (G'/G)-expansion method is advanced and easy tool for finding solution of NLEEs in engineering, optics and mathematical physics. The proposed method is highly effective and reliable.
VL  - 7
IS  - 1
ER  -

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Author Information

Attia Rani

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Munazza Saeed

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Muhammad Ashraf

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Rakshanda Zaman

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Qazi Mahmood-Ul-Hassan

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Kamran Ayub

Department of Mathematics, Riphah International University, Islamabad, Pakistan
Muhammad Yaqub Khan

Department of Mathematics, Riphah International University, Islamabad, Pakistan
Madiha Afzal

Department of Mathematics, Allama Iqbal Open University, Islamabad, Pakistan

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Plain Text BibTeX RIS

APA Style

Attia Rani, Munazza Saeed, Muhammad Ashraf, Rakshanda Zaman, Qazi Mahmood-Ul-Hassan, et al. (2018). Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method. Optics, 7(1), 43-53. https://doi.org/10.11648/j.optics.20180701.17

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ACS Style

Attia Rani; Munazza Saeed; Muhammad Ashraf; Rakshanda Zaman; Qazi Mahmood-Ul-Hassan, et al. Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method. Optics. 2018, 7(1), 43-53. doi: 10.11648/j.optics.20180701.17

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AMA Style

Attia Rani, Munazza Saeed, Muhammad Ashraf, Rakshanda Zaman, Qazi Mahmood-Ul-Hassan, et al. Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method. Optics. 2018;7(1):43-53. doi: 10.11648/j.optics.20180701.17

Copy | Download

@article{10.11648/j.optics.20180701.17,
  author = {Attia Rani and Munazza Saeed and Muhammad Ashraf and Rakshanda Zaman and Qazi Mahmood-Ul-Hassan and Kamran Ayub and Muhammad Yaqub Khan and Madiha Afzal},
  title = {Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method},
  journal = {Optics},
  volume = {7},
  number = {1},
  pages = {43-53},
  doi = {10.11648/j.optics.20180701.17},
  url = {https://doi.org/10.11648/j.optics.20180701.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.optics.20180701.17},
  abstract = {Nonlinear mathematical models and their solutions attain much attention in soliton theory. In this paper, main focus is to find travelling wave solutions of foam drainage equation and NLEE of fourth order. (G'/G)-expansion method is applied on these nonlinear differential equations. Wave transformation is used to convert nonlinear partial differential equation into an ordinary differential equation. It is observed that (G'/G)-expansion method is advanced and easy tool for finding solution of NLEEs in engineering, optics and mathematical physics. The proposed method is highly effective and reliable.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Solving Nonlinear Evolution Equations by (G'/G)-Expansion Method
AU  - Attia Rani
AU  - Munazza Saeed
AU  - Muhammad Ashraf
AU  - Rakshanda Zaman
AU  - Qazi Mahmood-Ul-Hassan
AU  - Kamran Ayub
AU  - Muhammad Yaqub Khan
AU  - Madiha Afzal
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.optics.20180701.17
DO  - 10.11648/j.optics.20180701.17
T2  - Optics
JF  - Optics
JO  - Optics
SP  - 43
EP  - 53
PB  - Science Publishing Group
SN  - 2328-7810
UR  - https://doi.org/10.11648/j.optics.20180701.17
AB  - Nonlinear mathematical models and their solutions attain much attention in soliton theory. In this paper, main focus is to find travelling wave solutions of foam drainage equation and NLEE of fourth order. (G'/G)-expansion method is applied on these nonlinear differential equations. Wave transformation is used to convert nonlinear partial differential equation into an ordinary differential equation. It is observed that (G'/G)-expansion method is advanced and easy tool for finding solution of NLEEs in engineering, optics and mathematical physics. The proposed method is highly effective and reliable.
VL  - 7
IS  - 1
ER  -

Copy | Download