Orbital stability of Camassa-Holm peakons in the background of a shallow-water system

We consider a class of traveling wave solutions to a shallow-water system. These waves exhibit corner singularities and hence linearized analysis is hard to apply to study their stability. We use a variational approach with the use of the Lyapunov method to provide a variational characterization and the orbital stability of these wave patterns. This is a joint work with Xiaochuan Liu, Yue Liu and Changzheng Qu.