  It is well-known that by requiring solutions of the Camassa--Holm equation to
satisfy a particular local conservation law for the energy in the weak sense,
one obtains what is known as conservative solutions. As conservative solutions
preserve energy, one might be inclined to think that any solitary traveling
wave is conservative. However, in this paper we prove that this is not true for
the traveling waves known as stumpons. We illustrate this result by comparing
the stumpon to simulations produced by a recently developed numerical scheme
for conservative solutions.
