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

Functional variable method and its applications for finding exact solutions of nonlinear PDEs in mathematical physics

Elsayed M. E. Zayed1*, Yaser A. Amer1 and Ahmed H. Arnous2
1Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt. 2Engineering Mathematics and Physics Department, Higher Institute of Engineering, El Shorouk, Egypt.
Email: [email protected]

  •  Published: 11 November 2013

Abstract

The functional variable method is a powerful mathematical tool for obtaining exact solutions of nonlinear evolution equations in mathematical physics. In this paper, the functional variable method is used to establish exact solutions of the (2+1)-dimensional Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation, the (3+1)-dimensional Burgers equation and the (3+1)- dimensional Jimbo-Miwa equation. The exact solutions of these four nonlinear equations including solitary wave solutions and periodic wave solutions are obtained. It is shown that the proposed method is effective and can be applied to many other nonlinear evolution equations. Comparison between our results obtained in this paper and the well-known results obtained by different authors using different methods are presented.

Key words: Functional variable method, nonlinear evolution equations, exact solutions, solitary wave solutions, Periodic wave solutions.

Abbreviation

AMS Subject Classification Code: 35K99, 35P05.