In fluid dynamics, the Camassa–Holm equation is the integrable, dimensionless and non-linear partial differential equation
The equation was introduced by Camassa and Holm as a bi-Hamiltonian model for waves in shallow water, and in this context the parameter κ is positive and the solitary wave solutions are smooth solitons.
In the special case that κ is equal to zero, the Camassa–Holm equation has peakon solutions: solitons with a sharp peak, so with a discontinuity at the peak in the wave slope.
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