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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〔Camassa & Holm 1993〕 == A family of equations with peakon solutions == The primary example of a PDE which supports peakon solutions is : where is the unknown function, and ''b'' is a parameter.〔Degasperis, Holm & Hone 2002〕 In terms of the auxiliary function defined by the relation , the equation takes the simpler form : This equation is integrable for exactly two values of ''b'', namely ''b'' = 2 (the Camassa–Holm equation) and ''b'' = 3 (the Degasperis–Procesi equation). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「peakon」の詳細全文を読む スポンサード リンク
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