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 modified simple equation method for solving nonlinear diffusive predator-prey system and Bogoyavlenskii equations

Elsayed M. E. Zayed
  • Elsayed M. E. Zayed
  • Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt.
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Yasser A. Amer
  • Yasser A. Amer
  • Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt.
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  •  Received: 08 December 2014
  •  Accepted: 02 February 2015
  •  Published: 28 February 2015

Abstract

The modified simple equation method (The modified SEM) is employed to find the exact traveling wave solutions involving parameters for two nonlinear evolution equations, namely, the diffusive predator-prey system and the Bogoyavlenskii equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified SEM provides an effective and a more powerful mathematical tool for solving nonlinear partial differential equations in mathematical physics. Our results in this paper are new and different from those obtained in the literature.

Key words: A diffusive predator-prey system, the Bogoyavlenskii equation, the modified SEM, traveling wave solutions, solitary wave solutions.