Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2758

Full Length Research Paper

The -expansion method and the exp -expansion method with applications to a higher order dispersive nonlinear Schrödinger equation

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: 23 February 2015
  •  Accepted: 17 March 2015
  •  Published: 30 March 2015

Abstract

In this article, we study the connection between the -expansion method and the exp -expansion method with the aid of a suitable transformation. We employ these two methods to derive families of exact solutions for a higher order dispersive nonlinear Schrödinger equation describing the propagation of the optical pulse in a medium. Comparison between these two methods is presented. We show that the two methods as well as their results are equivalent.
 
Key words: Higher order dispersive nonlinear Schrödinger equation, The -expansion method, the exp -expansion method, exact solutions.