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

Ding-jiang Huang and Hong-qing Zhang

Chaos, Solitons & Fractals, 2006, vol. 29, issue 4, 928-941

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:29:y:2006:i:4:p:928-941

DOI: 10.1016/j.chaos.2005.08.057

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