  A proof that strong solutions of the Dullin-Gottwald-Holm equation vanishing
on an open set of the (1+1) space-time are identically zero is presented. In
order to do it, we use a geometrical approach based on the conserved quantities
of the equation to prove a unique continuation result for its solutions. We
show that this idea can be applied to a large class of equations of the
Camassa-Holm type.
