Curvature blow-up and peakons for the Camassa–Holm type equation

In this paper we are concerned with a periodic Camassa–Holm type equation, which includes several integrable systems as particular cases such as the Camassa–Holm equation, the Novikov equation and the modified Camassa–Holm equation. By applying the method of characteristics, the blow-up criterion and the precise blow-up scenario are established. Then the curvature blow-up result is presented. Finally, periodic peakons are expressed in an explicit function formula. •Periodic peakons are calculated and expressed in an explicit function formula. .