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Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method
International Journal of Applied Mathematics and Theoretical Physics
Volume 3, Issue 2, April 2017, Pages: 20-25
Received: Feb. 4, 2017; Accepted: Feb. 21, 2017; Published: Mar. 14, 2017
Authors
A. K. M. Kazi Sazzad Hossain, Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
M. Ali Akbar, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
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Abstract
Exact solutions of nonlinear evolution equations (NLEEs) are very crucial to realize the obscurity of many physical phenomena in mathematical science. The modified simple equation (MSE) method is especially effective and highly proficient mathematical instrument to obtaining exact traveling wave solutions to NLEEs arising in science, engineering and mathematical physics. Though the modified simple equation method effectively provides exact traveling wave solutions to nonlinear evolution equations for balance number less or equal 2 but the method did not applied to solve if the balance number is greater than 2. In this article, the MSE method is executed to construct exact traveling wave solutions of nonlinear evolution equations namely Kuramoto-Sivashinsky equation with balance number equal to 3. The obtained solutions are expressed in terms of exponential and trigonometric functions including solitary and periodic solutions. Moreover the procedure of this method reduces huge volume of calculations.
Keywords
Modified Simple Equation (MSE) Method, Kuramoto-Sivashinsky Equation, Nonlinear Evolution Equations (NLEEs), Exact Traveling Wave Solutions
A. K. M. Kazi Sazzad Hossain, M. Ali Akbar, Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method, International Journal of Applied Mathematics and Theoretical Physics. Vol. 3, No. 2, 2017, pp. 20-25. doi: 10.11648/j.ijamtp.20170302.11
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