Peakon

In the theory of integrable systems, a peakon ("peaked soliton") is a soliton with discontinuous first derivative; the wave profile is shaped like the graph of the function . Some examples of non-linear partial differential equations with (multi-)peakon solutions are the Camassa–Holm shallow water wave equation, the Degasperis–Procesi equation and the Fornberg–Whitham equation. Since peakon solutions are only piecewise differentiable, they must be interpreted in a suitable weak sense. The concept was introduced in 1993 by Camassa and Holm in the short but much cited paper where they derived their shallow water equation. Peakon is also a village which beside Mobberley and also twinned with Pickford