  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

Fluid Dynamics;Exactly Solvable and Integrable Systems