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 e − | x | {displaystyle e^{-|x|}} . 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. 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 e − | x | {displaystyle e^{-|x|}} . 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.