Soliton Dynamics for the General Degasperis-Procesi Equation

摘要

We consider the general Degasperis-Procesi model of shallow water outflows. This fife parametric family of conservation laws contains, in particular, KdV, Camassa-Holm, and Degasperis-Procesi equations. The main result consists of a criterion which guarantees the existence of a smooth soliton-type solution. We discuss also the scenario of soliton interaction for this model in the nonintegrable case.