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

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

2012-03-18

arxiv.org/abs/1203.3917v3

Nonlinear Sciences

Pattern Formation and Solitons

9 pages, 2 figures

Scientific paper

It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves, which have been not found for other mainstream models of shallow water waves. In this letter, the closed-form solutions of peaked solitary waves of the KdV equation, the BBM equation and the Boussinesq equation are given, which have never been reported. All of them have either a peakon or an anti-peakon. Thus, the peaked solitary waves should be common for most of shallow water wave models, no matter whether or not they are integral and admit breaking-wave solutions. Especially, they have an unusual characteristic: phase speed of the peaked solitary waves has nothing to do with wave height. This is quite different from their traditional solitary waves with a smooth crest given by the mainstream models of shallow water waves.

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