Wave dynamics for peaked solitons of the Camassa–Holm equation

A detailed investigation of the wave dynamics for multiply peaked solitons of the Camassa–Holm equation is presented. The analysis proceeds in terms of the underlying component “peakons” using entirely elementary methods. The two-wave interactions exhibit intricate and subtle features such as role reversal, soliton absorption and annihilation, wave steepening and monodirectional propagation (for finite time) and a critical (amplitude) ratio. The discussion covers the entirety of these waveforms comprising two-peakon, peakon–antipeakon and two-antipeakon solutions. Their properties transfer to multipeakon dynamics and examples of three-wave interactions are given.