Blow-up phenomena for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions

摘要

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