Multi-component generalization of the Camassa–Holm equation

In this paper, we propose a multi-component system of the Camassa–Holm equation, denoted by CH(N,HN,H), with 2N2N components and an arbitrary smooth function HH. This system is shown to admit Lax pair and infinitely many conservation laws. We particularly study the case N=2N=2 and derive the bi-Hamiltonian structures and peaked soliton (peakon) solutions for some examples.