Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2764

Full Length Research Paper

Jacobi doubly periodic wave solutions for three versions of Benjamin-Bona- Mahony equation

M. A. Abdelkawy1*, M. A. Alghamdi2 and A. H. Bhrawy1,2
  1Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt. 2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
Email: [email protected]

  •  Accepted: 11 June 2012
  •  Published: 19 July 2012

Abstract

 

A variety of exact solutions for the Kadomtsov-Petviashvili- Benjamin-Bona-Mahony (KP-BBM) equation, nonlinear Zakharov-Kuznetsov- Benjamin-Bona-Mahony (ZK-BBM) equation and the generalized ZK-BBM equation are developed by means of the extended Jacobi elliptic function expansion method. Soliton and triangular periodic solutions can be established as the limits of Jacobi doubly periodic wave solutions.

 

Key words:  Jacobi elliptic function method, soliton and triangular periodic solutions, nonlinear dispersive Kadomtsov-Petviashvili- Benjamin-Bona-Mahony (KP-BBM) equation, nonlinear Zakharov-Kuznetsov- Benjamin-Bona-Mahony (ZK-BBM) equation, the generalized ZK-BBM equation.