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Mathematics 2016, 4(1), 6; doi:10.3390/math4010006

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation

1
Department of Mathematics, Pabna University of Science & Technology, Pabna 6600, Bangladesh
2
Department of Mathematics, Faculty of Basic Education, PAAET, Al-Ardhiya 92400, Kuwait
*
Author to whom correspondence should be addressed.
Academic Editor: Reza Abedi
Received: 24 November 2015 / Revised: 18 January 2016 / Accepted: 20 January 2016 / Published: 4 February 2016
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
View Full-Text   |   Download PDF [2933 KB, uploaded 4 February 2016]   |  

Abstract

In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs) describing microtubules, by implementing the exp(−Φ(ξ))-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ))-Expansion Method not disappointing in the least, is found and declared highly efficient. View Full-Text
Keywords: The exp(−Φ(ξ))-Expansion Method; models of microtubules; exact solutions; periodic solutions; rational solutions; solitary solutions; trigonometric solutions The exp(−Φ(ξ))-Expansion Method; models of microtubules; exact solutions; periodic solutions; rational solutions; solitary solutions; trigonometric solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Alam, N.; Belgacem, F.B.M. Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation. Mathematics 2016, 4, 6.

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