Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2752

Full Length Research Paper

Improved (G’/G)- expansion method for constructing exact traveling wave solutions for a nonlinear PDE of nanobiosciences

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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  •  Accepted: 20 August 2013
  •  Published: 25 August 2013

Abstract

In the present paper, the improved (G’/G) - expansion method combined with suitable transformations is used to construct many exact solutions involving parameters of a nonlinear equation describing the nano-ionic currents along microtublues. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with parameters are obtained. When these parameters are taken as special values, some solitary wave solutions and the periodic wave solution are derived from the exact solutions. This method can be employed for many other nonlinear evolution equations in mathematical physics and engineering. Comparisons between our results and the well-known results are given.

 

Key words: Improved (G’/G) - expansion method, exact traveling wave solutions, solitary and periodic solutions, nano-ionic currents along microtublues, nanobiosciences.