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

Exact solutions for the nonlinear KPP equation by using the Riccati equation method combined with the G'/G - expansion method

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.
  • Google Scholar


  •  Received: 15 January 2015
  •  Accepted: 05 February 2015
  •  Published: 15 February 2015

Abstract

The improved Riccati equation method combined with the improved  - expansion method is an interesting approach to find more general exact solutions of the nonlinear evolution equations in mathematical physics. The objective of this article is to employ this method to construct exact solutions involving parameters of a nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation. When these parameters are taken to be special values, the solitary wave solutions, the periodic wave solutions and the rational function solutions are derived from the exact solutions. The proposed method appears to be effective for solving other nonlinear evolution equations in the mathematical physics.
 
Key words:  The Riccati equation method,  the  - expansion method, the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation, exact solutions, solitary wave solutions, periodic wave solutions, rational solutions.
   
PACS: 02.30.Jr, 05.45.Yv, 02.30.Ik.