International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

The generalized projective Riccati equations method and its applications for solving two nonlinear PDEs describing microtubules

Elsayed M. E. Zayed
  • Elsayed M. E. Zayed
  • Department of Mathematics, Faculty of Science, Zagazig University P. O. Box 44519, Zagazig, Egypt.
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Khaled A. E. Alurrfi
  • Khaled A. E. Alurrfi
  • Department of Mathematics, Faculty of Science, Zagazig University P. O. Box 44519, Zagazig, Egypt.
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  •  Received: 27 February 2015
  •  Accepted: 10 June 2015
  •  Published: 16 July 2015

Abstract

Microtubules (MTs) are major cytoskeletal proteins. They are hollow cylinders formed by protofilaments (PFs) representing series of proteins known as tubulin dimers. Each dimer is an electric dipole. These diamers are in a straight position within PFs or in radially displaced positions pointing out of cylindrical surface. In this paper, the authors demonstrate how the generalized projective Riccati equations method can be used in the study of the nonlinear dynamics of MTs. To this end, the authors apply this method to construct the exact solutions with parameters for two nonlinear PDEs describing MTs. The first equation describes the model of microtubules as nanobioelectronics transmission lines. The second equation describes the dynamics of radial dislocations in microtubules. As a result, hyperbolic, trigonometric and rational function solutions are obtained. When these parameters are taken as special values, solitary wave solutions are derived from the exact solutions. Comparison between our recent results and the well-known results is given.
 
Key words: Generalized projective Riccati equations method, models of microtubules (MTs), exact solutions, solitary solutions, trigonometric solutions rational solutions.