Numerical simulation of Camassa–Holm peakons by adaptive upwinding

The Camassa–Holm equation is a conservation law with a non-local flux that models shallow water waves and features soliton solutions with a corner at their crests, so-called peakons. In the present paper a finite-volume method is developed to simulate the dynamics of peakons. This conservative scheme is adaptive, high resolution and stable without any explicit introduction of artificial viscosity. A numerical simulation indicates that a certain plateau shaped travelling wave solution breaks up in time.