Although the modified simple equation method effectively provides exact traveling wave solutions to nonlinear evolution equations in the field of engineering and mathematical physics, it has some drawbacks. Particularly, if the balance number is greater than 1, the method cannot be expected to yield any solution. In this article, we present a process to implement the modified simple equation method to solve nonlinear evolution equations for balance number greater than 1, namely with balance number equal to 2. To validate our theory through applications, two equations have been chosen to undergo the proposed process, the Boussinesq and the Fisher equations, to which traveling wave are found and analyzed. For special parameters values, solitary wave solutions are originated from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process.
Published in | Mathematics Letters (Volume 2, Issue 1) |
DOI | 10.11648/j.ml.20160201.11 |
Page(s) | 1-18 |
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. |
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Copyright © The Author(s), 2016. Published by Science Publishing Group |
Boussinesq Equation, Fisher Equation, Modified Simple Equation Method, Nonlinear Evolution Equations, Solitary Wave Solutions
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APA Style
Md. Ashrafuzzaman Khan, M. Ali Akbar, Fethi Bin Muhammad Belgacem. (2016). Solitary Wave Solutions for the Boussinesq and Fisher Equations by the Modified Simple Equation Method. Mathematics Letters, 2(1), 1-18. https://doi.org/10.11648/j.ml.20160201.11
ACS Style
Md. Ashrafuzzaman Khan; M. Ali Akbar; Fethi Bin Muhammad Belgacem. Solitary Wave Solutions for the Boussinesq and Fisher Equations by the Modified Simple Equation Method. Math. Lett. 2016, 2(1), 1-18. doi: 10.11648/j.ml.20160201.11
@article{10.11648/j.ml.20160201.11, author = {Md. Ashrafuzzaman Khan and M. Ali Akbar and Fethi Bin Muhammad Belgacem}, title = {Solitary Wave Solutions for the Boussinesq and Fisher Equations by the Modified Simple Equation Method}, journal = {Mathematics Letters}, volume = {2}, number = {1}, pages = {1-18}, doi = {10.11648/j.ml.20160201.11}, url = {https://doi.org/10.11648/j.ml.20160201.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160201.11}, abstract = {Although the modified simple equation method effectively provides exact traveling wave solutions to nonlinear evolution equations in the field of engineering and mathematical physics, it has some drawbacks. Particularly, if the balance number is greater than 1, the method cannot be expected to yield any solution. In this article, we present a process to implement the modified simple equation method to solve nonlinear evolution equations for balance number greater than 1, namely with balance number equal to 2. To validate our theory through applications, two equations have been chosen to undergo the proposed process, the Boussinesq and the Fisher equations, to which traveling wave are found and analyzed. For special parameters values, solitary wave solutions are originated from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process.}, year = {2016} }
TY - JOUR T1 - Solitary Wave Solutions for the Boussinesq and Fisher Equations by the Modified Simple Equation Method AU - Md. Ashrafuzzaman Khan AU - M. Ali Akbar AU - Fethi Bin Muhammad Belgacem Y1 - 2016/06/03 PY - 2016 N1 - https://doi.org/10.11648/j.ml.20160201.11 DO - 10.11648/j.ml.20160201.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 1 EP - 18 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20160201.11 AB - Although the modified simple equation method effectively provides exact traveling wave solutions to nonlinear evolution equations in the field of engineering and mathematical physics, it has some drawbacks. Particularly, if the balance number is greater than 1, the method cannot be expected to yield any solution. In this article, we present a process to implement the modified simple equation method to solve nonlinear evolution equations for balance number greater than 1, namely with balance number equal to 2. To validate our theory through applications, two equations have been chosen to undergo the proposed process, the Boussinesq and the Fisher equations, to which traveling wave are found and analyzed. For special parameters values, solitary wave solutions are originated from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process. VL - 2 IS - 1 ER -