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Link between travelling waves and first order nonlinear ordinary differential equation with a sixth-degree nonlinear term

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  • Huang, Ding-jiang
  • Zhang, Hong-qing

Abstract

Many travelling wave solutions of nonlinear evolution equations can be written as a polynomial in several elementary or special functions which satisfy a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. From that property, we deduce an algebraic method for constructing those solutions by determining only a finite number of coefficients. Being concise and straightforward, the method is applied to three nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.

Suggested Citation

  • Huang, Ding-jiang & Zhang, Hong-qing, 2006. "Link between travelling waves and first order nonlinear ordinary differential equation with a sixth-degree nonlinear term," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 928-941.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:4:p:928-941
    DOI: 10.1016/j.chaos.2005.08.057
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