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It is well-known that the celebrated Camassa-Holm equation has the peakedsolitary waves, which have been not reported for other mainstream models ofshallow water waves. In this letter, the closed-form solutions of peakedsolitary waves of the KdV equation, the BBM equation and the Boussinesqequation are given for the first time. All of them have either a peakon or ananti-peakon. Each of them exactly satisfies the corresponding Rankine-Hogoniotjump condition and should be understood as weak solution. Therefore, the peakedsolitary waves might be common for most of shallow water wave models, no matterwhether or not they are integrable and/or admit breaking-wave solutions.

Two kinds of peaked solitary waves of the KdV, BBM and Boussinesq equations