Traveling wave solutions of the Camassa-Holm equation (Q2575071)

The Camassa-Holm equation (CHE) arises as a model for the unidirectional propagation of shallow water waves over a flat bottom, as well as a model for nonlinear waves in a cylindrical axially symmetric hyperelastic rod. CHE is a bi-Hamiltonian equation with infinitely many conservation laws. The author studies traveling wave solutions of the CHE using a natural weak formulation. It is shown that, in addition to smooth solutions, there are a multitude of traveling waves with singularities: peakons, cuspons, stumpons, and composite waves.