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A novel class of solutions for a non-linear third order wave equation generated by the Weierstraß transformation

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  • Huber, Alfred

Abstract

In this paper, a traveling wave reduction combined with the transformation method in terms of Weierstraß elliptic functions is used to find a class of new exact solutions for a non-linear partial differential equation (nPDE) of third order, the so called combined KdV–mKdV equation. The usual starting point is a special transformation (the traveling wave “ansatz”) converting the nPDG in its two variables x and t to the belonging non-linear ordinary differential equation (nODE) in the single variable ξ. Using the Weierstraß elliptic-function method, new exact class of solutions in terms of the function ℘(ξ;g2,g3) are obtained. Moreover, class of solutions showing typical solitary behavior results as a special case.

Suggested Citation

  • Huber, Alfred, 2006. "A novel class of solutions for a non-linear third order wave equation generated by the Weierstraß transformation," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 972-978.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:972-978
    DOI: 10.1016/j.chaos.2005.08.189
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