Coupled Camassa–Holm equations, -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.