Wave-breaking and persistence properties in weighted L^P spaces for a Camassa-Holm type equation with quadratic and cubic nonlinearities

We consider the Cauchy problem of a Camassa-Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted L-p spaces.