On peaked solitary waves of Camassa-Holm equation

Shijun Liao

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arXiv · 1204.4517

On peaked solitary waves of Camassa-Holm equation

Shijun Liao

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Abstract

Unlike the Boussinesq, KdV and BBM equations, the celebrated Casamma-Holm (CH) equation can model both phenomena of soliton interaction and wave breaking. Especially, it has peaked solitary waves in case of omega=0. Besides, in case of omega > 0, its solitary wave "becomes $C^\infty$ and there is no derivative discontinuity at its peak", as mentioned by Camassa and Holm in 1993 (PRL). However, it is found in this article that the CH equation has peaked solitary waves even in case of omega > 0. Especially, all of these peaked solitary waves have an unusual property: their phase speeds have nothing to do with the height of peakons or anti-peakons. Therefore, in contrast to the traditional view-points, the peaked solitary waves are a common property of the CH equation: in fact, all mainstream models of shallow water waves admit such kind of peaked solitary waves

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Shijun Liao. 2012-04-20. On peaked solitary waves of Camassa-Holm equation. https://arxiv.org/abs/1204.4517

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