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Peakon

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Is Peakon really anonymous??

In the theory of integrable systems, a peakon 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.
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    • A family of equations with peakon solutions 

    • The single peakon solution 

    • Multipeakon solutions 

    • Explicit solution formulas