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arXiv · 1101.1605

Negative order KdV equation with both solitons and kink wave solutions

Zhijun Qiao·Jibin Li
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Abstract

In this paper, we report an interesting integrable equation that has both solitons and kink solutions. The integrable equation we study is $(\frac{-u_{xx}}{u})_{t}=2uu_{x}$, which actually comes from the negative KdV hierarchy and could be transformed to the Camassa-Holm equation through a gauge transform. The Lax pair of the equation is derived to guarantee its integrability, and furthermore the equation is shown to have classical solitons, periodic soliton and kink solutions.

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BibTeXRIS

Zhijun Qiao, Jibin Li. 2011-04-13. Negative order KdV equation with both solitons and kink wave solutions. https://doi.org/10.1209/0295-5075%2F94%2F50003

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