Invariants and wave breaking analysis of a Camassa-Holm type equation with quadratic and cubic nonlinearities

A non-local evolution equation of the Camassa-Holm type with dissipation is considered. The local well-posedness of the solutions of the Cauchy problem involving the equation is established via Kato's approach and the wave breaking scenario is also described. To prove such result, we firstly construct conserved currents for the equation and from them, conserved quantities.