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A Generalized and Improved -Expansion Method for Nonlinear Evolution Equations

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  • M. Ali Akbar
  • Norhashidah Hj. Mohd. Ali
  • E. M. E. Zayed

Abstract

A generalized and improved -expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.

Suggested Citation

  • M. Ali Akbar & Norhashidah Hj. Mohd. Ali & E. M. E. Zayed, 2012. "A Generalized and Improved -Expansion Method for Nonlinear Evolution Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-22, March.
    • Handle: RePEc:hin:jnlmpe:459879
    DOI: 10.1155/2012/459879
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    Cited by:

    1. Li, Jiayang & Zhang, Zhikun & Dai, Min & Ming, Ju & Wang, Xiangjun, 2023. "Diffusion equations with Markovian switching: Well-posedness, numerical generation and parameter inference," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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