Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2748

Full Length Research Paper

The improved generalized Riccati equation mapping method and its application for solving a nonlinear partial differential equation (PDE) describing the dynamics of ionic currents along microtubules

Elsayed M. E. Zayed
  • Elsayed M. E. Zayed
  • Mathematics Department, Faculty of Sciences, Zagazig University, Zagazig, Egypt.
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Yasser A. Amer
  • Yasser A. Amer
  • Mathematics Department, Faculty of Sciences, Zagazig University, Zagazig, Egypt.
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Reham M. A. Shohib
  • Reham M. A. Shohib
  • Mathematics Department, Faculty of Sciences, Zagazig University, Zagazig, Egypt.
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  •  Received: 10 December 2013
  •  Accepted: 10 April 2014
  •  Published: 30 April 2014

Abstract

In this paper we apply the improved Riccati equation mapping method to construct many families of exact solutions of a nonlinear partial differential equation involving parameters of a special interest in nanobiosciences and biophysics which describe a model of microtubules as nonlinear RLC transmission lines. As results, we can successfully recover the previously known results that have been found using other methods. This method is straightforward and concise, and it can be applied to other nonlinear PDEs in mathematical physics. Comparison between our new results and the well-known results are given. Some comments on the well-known results are also presented at the end of this article.

 

Key words: Improved Riccati equation mapping method, exact traveling wave solutions, nonlinear partial differential equations (PDEs) of microtubules, Nonlinear RLC transmission lines.

 

PACS: 02.30.Jr, 05.45.Yv, 02.30.Ik