Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2750

Full Length Research Paper

Double traveling wave solutions for some nonlinear partial differential equations in mathematical Physics

E.M.E. Zayed1, Khaled A. Gepreel1,2* and Fawziah M. Al-Otaibi2
¹Mathematics Department, Faculty of Science, Zagazig University, Egypt. ²Mathematics Department, Faculty of Science, Taif University, Saudi Arabia.
Email: [email protected]

  •  Accepted: 14 September 2012
  •  Published: 19 November 2012

Abstract

In this article, we construct the double soliton exact solutions for some nonlinear partial differential equations in mathematical physics via (2+1)-dimensional Painleve integrable Burgers equations, (2+1)-dimensional breaking soliton equations and (2+1)-dimensional Nizhnik-Novikov Veselov equations. We obtain many new types of complexiton soliton solution, that is, various combination of trigonometric periodic function and hyperbolic function, various combination of trigonometric periodic function and rational function, various combination of hyperbolic function and rational function solutions.

 

Key words: Double soliton solution, the traveling wave solution, the (2+1)-dimensional Painleve integrable Burgers equations, the (2+1)-dimensional breaking soliton equations and the (2+1)-dimensional Nizhnik-Novikov Veselov equations.