Coupled Camassa-Holm equations, N-peakons and infinitely many conservation laws

Three coupled Camassa-Holm equations are proposed, which are associated with a 4×4 matrix spectral problem with two potentials. With the aid of the zero-curvature equation, we derive a hierarchy of new nonlinear evolution equations and establish their bi-Hamiltonian structures. The three coupled Camassa-Holm equations are exactly negative flows in the hierarchy, and exact solutions with N-peakons and infinite sequences of conserved quantities are discussed.