A three-component Camassa-Holm system with cubic nonlinearity and peakons

摘要

In this paper, we propose a three-component Camassa-Holm (3CH) system with cubic nonlinearity and peaked solitons (peakons). The 3CH model is proven to be integrable in the sense of Lax pair, Hamiltonian structure, and conservation laws. We show that this system admits peakons and multi-peakon solutions. Additionally, reductions of the 3CH system are investigated so that a new integrable perturbed CH equation with cubic nonlinearity is generated to possess peakon solutions.