Camassa-Holm Cuspons, Solitons and Their Interactions via the Dressing Method

A dressing method is applied to a matrix Lax pair for the Camassa-Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa-Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.