Camassa–Holm Equation

In fluid dynamics, the Camassa–Holm equation is the integrable, dimensionless and non-linear partial differential equation


u_t + 2kappa u_x - u_{xxt} + 3 u u_x = 2 u_x_u_{xx} + u u_{xxx}. ,

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.

Read more about Camassa–Holm Equation:  Relation To Waves in Shallow Water, Hamiltonian Structure, Integrability, Exact Solutions, Wave Breaking, Long-time Asymptotics

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