  This paper is devoted to an integrable two-component Camassa-Holm system with
cubic nonlinearity, which includes the cubic Camassa-Holm equation (also called
the Fokas-Olver-Rosenau-Qiao equation) as a special case. The one peaked
solitons (peakons) and two peakon solutions are described in an explicit
formula. Then, the local well-posedness for the Cauchy problem of the system is
studied. Moreover, we target at the precise blow-up scenario for strong
solutions to the system, and establish a new blow-up result with respect to the
initial data.
