### Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method

Received: Feb. 04, 2017    Accepted: Feb. 21, 2017    Published: Mar. 14, 2017

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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.

 DOI 10.11648/j.ijamtp.20170302.11 Published in International Journal of Applied Mathematics and Theoretical Physics ( Volume 3, Issue 2, April 2017 ) Page(s) 20-25 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

Modified Simple Equation (MSE) Method, Kuramoto-Sivashinsky Equation, Nonlinear Evolution Equations (NLEEs), Exact Traveling Wave Solutions

References
• APA Style

A. K. M. Kazi Sazzad Hossain, M. Ali Akbar. (2017). Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method. International Journal of Applied Mathematics and Theoretical Physics, 3(2), 20-25. https://doi.org/10.11648/j.ijamtp.20170302.11

ACS Style

A. K. M. Kazi Sazzad Hossain; M. Ali Akbar. Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method. Int. J. Appl. Math. Theor. Phys. 2017, 3(2), 20-25. doi: 10.11648/j.ijamtp.20170302.11

AMA Style

A. K. M. Kazi Sazzad Hossain, M. Ali Akbar. Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method. Int J Appl Math Theor Phys. 2017;3(2):20-25. doi: 10.11648/j.ijamtp.20170302.11

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author = {A. K. M. Kazi Sazzad Hossain and M. Ali Akbar},
title = {Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method},
journal = {International Journal of Applied Mathematics and Theoretical Physics},
volume = {3},
number = {2},
pages = {20-25},
doi = {10.11648/j.ijamtp.20170302.11},
url = {https://doi.org/10.11648/j.ijamtp.20170302.11},
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.},
year = {2017}
}
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T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
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AB  - 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.
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Author Information
• Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh

• Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

• Section