A three-component generalization of Camassa-Holm equation with N-peakon solutions

A three-component generalization of Camassa-Holm equation with peakon solutions is proposed, which is associated with a 3×3 matrix spectral problem with three potentials. With the aid of the zero-curvature equation, we derive a hierarchy of new nonlinear evolution equations and establish their Hamiltonian structures. The three-component generalization of Camassa-Holm equation is exactly a negative flow in the hierarchy and admits exact solutions with N-peakons and an infinite sequence of conserved quantities.