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Solitary Wave Solutions for the Boussinesq and Fisher Equations by the Modified Simple Equation Method
Mathematics Letters
Volume 2, Issue 1, February 2016, Pages: 1-18
Received: Nov. 14, 2015; Accepted: Mar. 30, 2016; Published: Jun. 3, 2016
Authors
Md. Ashrafuzzaman Khan, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
M. Ali Akbar, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Fethi Bin Muhammad Belgacem, Department of Mathematics, Faculty of Basic Education, PAAET, Al-Ardhyia, Kuwait
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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.
Keywords
Boussinesq Equation, Fisher Equation, Modified Simple Equation Method, Nonlinear Evolution Equations, Solitary Wave Solutions
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, Mathematics Letters. Vol. 2, No. 1, 2016, pp. 1-18. doi: 10.11648/j.ml.20160201.11
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