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Exact and Solitary Wave Solutions to the Generalized Fifth-order KdV Equation by Using the Modified Simple Equation Method
Applied and Computational Mathematics
Volume 4, Issue 3, June 2015, Pages: 122-129
Received: Apr. 10, 2015; Accepted: Apr. 21, 2015; Published: Apr. 30, 2015
Authors
M. Ashrafuzzaman Khan, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
M. Ali Akbar, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
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Abstract
Although the modified simple equation (MSE) method effectively provides exact traveling wave solutions to nonlinear evolution equations (NLEEs) in the field of engineering and mathematical physics, it has some limitations. When the balance number is greater than one, usually the method does not give any solution. In this article, we have exposed a process how to implement the MSE method to solve NLEEs for balance number two. In order to verify the process, the generalized fifth-order KdV equation has been solved. By means of this scheme, we found some fresh traveling wave solutions to the above mentioned equation. When the parameters receive special values, solitary wave solutions are derived 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
MSE Method, Nonlinear Evolution Equations, Solitary Wave Solutions, Exact Solutions, Generalized Fifth-Order Kdv Equation
M. Ashrafuzzaman Khan, M. Ali Akbar, Exact and Solitary Wave Solutions to the Generalized Fifth-order KdV Equation by Using the Modified Simple Equation Method, Applied and Computational Mathematics. Vol. 4, No. 3, 2015, pp. 122-129. doi: 10.11648/j.acm.20150403.14
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