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Applications of an Extended ( ð º â€² / ð º ) -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics

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  • E. M. E. Zayed
  • Shorog Al-Joudi

Abstract

We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended ( ð º î…ž / ð º ) -expansion method, where G satisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

Suggested Citation

  • E. M. E. Zayed & Shorog Al-Joudi, 2010. "Applications of an Extended ( ð º â€² / ð º ) -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, August.
    • Handle: RePEc:hin:jnlmpe:768573
    DOI: 10.1155/2010/768573
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    Cited by:

    1. Muhammad Shakeel & Attaullah & Essam Roshdy El-Zahar & Nehad Ali Shah & Jae Dong Chung, 2022. "Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves," Mathematics, MDPI, vol. 10(7), pages 1-17, March.

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